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| Meta Title | Log Base 2 Calculator | |||||||||||||||
| Meta Description | The log base 2 calculator quickly computes the value of the logarithm function with base two, i.e., log₂(x) for arbitrary (positive) x. | |||||||||||||||
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| Boilerpipe Text | Table of contents
What is a logarithm?
Binary logarithm
FAQs
Welcome to Omni's
log base 2 calculator
. Your favorite tool to calculate the value of
log₂(x)
for arbitrary (positive)
x
. The operation is a special case of the logarithm, i.e., when the log's base is equal to
2
. As such, we sometimes call it
the binary logarithm
. If you wish to discover the more general case or know about the log rules, check out our
log calculator
and our article "
Log Rules Made Simple: Understanding the Laws of Logarithms
".
So what is, e.g., the log with base
2
of
8
? Or
log₂ 16
? Or
log₂ 32
? Well, let's jump straight into the article and find out!
What is a logarithm?
As soon as humanity learned to add numbers, it found a way to simplify the notation for
adding the same number
several times: multiplication.
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 8 × 5
Then, an obvious question appeared: how could we write
multiplying the same number
several times? And again, there came some smart mathematicians who introduced exponents.
5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = 5⁸
However, there is always that
one curious person
who asks the wildest questions. In this case, they wondered if there was a way to
invert all these operations
. Lucky for us, mathematics, and the whole world of science, other curious people found the answer.
For addition, it was easy: the inverse operation is
subtraction
. For multiplication, it's still pretty simple: it's division. For exponents, however, the story gets
more complicated
. After all, we know that
5 + 8 = 8 + 5
and
5 × 8 = 8 × 5
, but
5⁸
is very different from
8⁵
. So what should the inverse operation give? If we have
5⁸
, should it return
5
or
8
?
The logarithm
(of base
5
) would be the operation if we chose option
8
. In other words, it is
a function that tells you the exponent needed to obtain the value
. Symbolically, we can write the definition like so:
💡
logₐ(b)
gives you the power to which you'd need to raise
a
in order to obtain
b
. Note, however, that, in general, this can be a fractional exponent!
For comparison, the inverse operation that would return the
5
from
5⁸
would be simply the (
8
-th) root. If we wanted to get
a bit more technical
, then we could say that, in general, if we had an expression
xʸ
, then the root is the inverse operation for
x
, while the logarithm is that for
y
. And if we wanted to get
even more technical
, we'd say that the first inverts a polynomial function, while the latter inverts an exponential one.
Before we move further, let us have a pretty bullet list with
a few vital points of information about our new friend, the logarithm function
.
There are
two very special cases of the logarithm
which have unique notation:
the natural logarithm
and the logarithm with base
10
. We denote them
ln(x)
and
log(x)
(the second one simply without the small
10
), and their bases are, respectively, the Euler number
e
and (surprise, surprise!) the number
10
.
While the latter is obvious, the former may pose some problems – if you're not sure what the number
e
is, check out our
e calculator
.
The logarithm function is defined only for positive numbers.
In other words, whenever we write
logₐ(b)
, we require
b
to be positive.
Whatever the base,
the logarithm of
1
is equal to
0
. After all, whatever we raise to power
0
, we get
1
. To learn how to change the base of your logarithm, access the article "
Change-of-base Formula Made Easy
".
Logarithms are extremely important.
And we mean
EXTREMELY
important. Outside of mathematics, they're used in
statistics
(e.g., the lognormal distribution),
economy
(e.g., the GDP index),
medicine
(e.g., the QUICKI index), and
chemistry
(e.g., the half-life decay). Also, quite
a few physical units
are based on logarithms, for instance, the Richter scale, the pH scale, and the dB scale.
Today, we'll focus on
a very special case of the logarithm
, i.e., base
2
, which we sometimes call
the binary logarithm
. In essence, we'll focus on taking the powers of
2
and… Well, on second thought, why don't we dedicate
a whole section
to this one?
Binary logarithm
As mentioned at the end of
the above section
,
the binary logarithm is a special case of the logarithmic function with base
2
. That means that we'll have expressions of the form
log₂(x)
, and we'll ask ourselves to what power we should raise
2
in order to obtain
x
. For instance, we can easily observe that
log₂ 4 = 2
.
Seemingly,
2
is
a number like any other
. However, it has some interesting properties. E.g., it is the smallest prime number and the only even one. Moreover, it's the base for any computer-related operations via the binary representation.
Since it's so important, let's recall
a few basic powers of
2
. Remember that the exponent can also be
0
or even negative.
x
-3
-2
-1
0
1
2
3
4
5
6
7
8
2
x
⅛
¼
½
1
2
4
8
16
32
64
128
256
Now we can see
some more examples
than just the
log₂ 4 = 2
from above. For instance, we can say that the log with base
2
of
8
is
3
. Similarly,
log₂ 16 = 4
or
log₂ 32 = 5
.
But what is, say, log₂ 5?
Surely,
5
is not a power of
2
.
To be precise,
it's not an integer power of
2
. We have to remember that there are also fractional exponents, and indeed, here, we need one of those. Unfortunately,
they're not so simple to guess
. In some cases, we can try to use tricks like the change of base rule, but, in general, it's best to use an external tool — something like our
log base 2 calculator
or the
change of base formula calculator
.
In it, you can see
two variable windows
:
x
and
log₂(x)
. Hopefully, the notation is self-explanatory. For example, if you'd like to find
log₂ 16
, you need to input
16
under
x
, and the calculator will give you the answer in the other window. If you require
log₂ 32
, you enter
32
. Also, note how Omni's log base 2 calculator
works both ways
: you can either input the value of
x
and obtain
log₂(x)
or the other way round.
That'll be enough for today's lesson.
Go, my young padawan, and make sure to play around with the calculator or any other algebra-related tool that we have on offer.
FAQs
How do I calculate the logarithm in base 2?
To calculate the logarithm in base 2, you probably need a calculator. However, if you know the result of the natural logarithm or the base 10 logarithm of the same argument, you can follow these easy steps to find the result. For a number
x
:
Find the result of either
log10(x)
or
ln(x)
.
Divide
the result of the previous step by the corresponding value between:
log10(2) = 0.30103
; or
ln(2) = 0.693147
.
The result of the division is
log2(x)
.
What is the logarithm in base 2 of 256?
The logarithm in base 2 of
256
is
8
. To find this result, consider the following formula:
2
x
= 256
The logarithm corresponds to the following equation:
log2(256) = x
In this case, we can check the powers of 2 to see if we can find the value of
x
:
2
0
= 1
,
2
1
= 2
,
2
2
= 4
, …,
2
7
= 128
, and
2
8
= 256
.
Since we found the argument of our logarithm, we can write that:
log2(256) = 8
.
Why is the logarithm in base 2 important?
In a computer world, binary code is of essential importance: words, numbers, pictures, and everything else can be reduced to a string of 0s and 1s. Since the binary code uses only
two digits
, the number 2 appears consistently in computer science.
The widespread appearance of log2 in computer science has no strong mathematical reason (since logarithms can change base by multiplication) but can be useful. For example, using log2 to compute entropy allows us to obtain the result expressed in bits, which are the natural unit.
What is the difference between ln and log2?
The difference between ln and log2 is the
base
. The logarithm is the
inverse operation of exponentiation
, that is, the power of a number, and it answers the question: "what is the exponent that produces a given result?".
The base of the logarithm is the number to which you apply the exponent: in the case of ln, the number is
e
, Neper's number. For log2, you must consider the number
2
. To sum up:
If
b = ln(x)
, then
e
b
= x
; and
If
c = log2(x)
, then
2
c
= x
. | |||||||||||||||
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# Log Base 2 Calculator
Creators
Maciej Kowalski, PhD
Maciej KowalskiPhD
LinkedIn
Research Gate
Maciej holds a PhD in Theoretical Mathematics from the Polish Academy of Sciences. He loves patterns and structure, be it in datasets, equations, or everyday life. He is curious and meticulous, and balances his analytical side with a passion for fantasy, CrossFit, good cinema, and a diverse array of games. [See full profile](https://www.omnicalculator.com/authors/maciej-kowalski)
Check our [editorial policy](https://www.omnicalculator.com/editorial-policies)
Reviewers
Steven Wooding
Steven Wooding
LinkedIn
Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. [See full profile](https://www.omnicalculator.com/authors/steven-wooding)
Check our [editorial policy](https://www.omnicalculator.com/editorial-policies)
2 283 people find this calculator helpful
2K
Table of contents
- [What is a logarithm?](https://www.omnicalculator.com/math/log-2#what-is-a-logarithm)
- [Binary logarithm](https://www.omnicalculator.com/math/log-2#binary-logarithm)
- [FAQs](https://www.omnicalculator.com/math/log-2#faqs)
Welcome to Omni's **log base 2 calculator**. Your favorite tool to calculate the value of **log₂(x)** for arbitrary (positive) **x**. The operation is a special case of the logarithm, i.e., when the log's base is equal to **2**. As such, we sometimes call it **the binary logarithm**. If you wish to discover the more general case or know about the log rules, check out our [log calculator](https://www.omnicalculator.com/math/log) and our article "[Log Rules Made Simple: Understanding the Laws of Logarithms](https://www.omnicalculator.com/log-rules)".
So what is, e.g., the log with base **2** of **8**? Or **log₂ 16**? Or **log₂ 32**? Well, let's jump straight into the article and find out\!
## What is a logarithm?
As soon as humanity learned to add numbers, it found a way to simplify the notation for **adding the same number** several times: multiplication.
**5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 8 × 5**
Then, an obvious question appeared: how could we write **multiplying the same number** several times? And again, there came some smart mathematicians who introduced exponents.
**5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = 5⁸**
However, there is always that **one curious person** who asks the wildest questions. In this case, they wondered if there was a way to **invert all these operations**. Lucky for us, mathematics, and the whole world of science, other curious people found the answer.
For addition, it was easy: the inverse operation is **subtraction**. For multiplication, it's still pretty simple: it's division. For exponents, however, the story gets **more complicated**. After all, we know that **5 + 8 = 8 + 5** and **5 × 8 = 8 × 5**, but **5⁸** is very different from **8⁵**. So what should the inverse operation give? If we have **5⁸**, should it return **5** or **8**?
**The logarithm** (of base **5**) would be the operation if we chose option **8**. In other words, it is **a function that tells you the exponent needed to obtain the value**. Symbolically, we can write the definition like so:
💡 **logₐ(b)** gives you the power to which you'd need to raise **a** in order to obtain **b**. Note, however, that, in general, this can be a fractional exponent\!
For comparison, the inverse operation that would return the **5** from **5⁸** would be simply the (**8**\-th) root. If we wanted to get **a bit more technical**, then we could say that, in general, if we had an expression **xʸ**, then the root is the inverse operation for **x**, while the logarithm is that for **y**. And if we wanted to get **even more technical**, we'd say that the first inverts a polynomial function, while the latter inverts an exponential one.
Before we move further, let us have a pretty bullet list with **a few vital points of information about our new friend, the logarithm function**.
- There are **two very special cases of the logarithm** which have unique notation: [the natural logarithm](https://www.omnicalculator.com/math/natural-log) and the logarithm with base **10**. We denote them **ln(x)** and **log(x)** (the second one simply without the small **10**), and their bases are, respectively, the Euler number **e** and (surprise, surprise!) the number **10**.
*While the latter is obvious, the former may pose some problems – if you're not sure what the number **e** is, check out our [e calculator](https://www.omnicalculator.com/math/e-power-x).*
- **The logarithm function is defined only for positive numbers.** In other words, whenever we write **logₐ(b)**, we require **b** to be positive.
- Whatever the base, **the logarithm of** **1** **is equal to** **0**. After all, whatever we raise to power **0**, we get **1**. To learn how to change the base of your logarithm, access the article "[Change-of-base Formula Made Easy](https://www.omnicalculator.com/change-of-base-formula)".
- **Logarithms are extremely important.** And we mean **EXTREMELY** important. Outside of mathematics, they're used in **statistics** (e.g., the lognormal distribution), **economy** (e.g., the GDP index), **medicine** (e.g., the QUICKI index), and **chemistry** (e.g., the half-life decay). Also, quite **a few physical units** are based on logarithms, for instance, the Richter scale, the pH scale, and the dB scale.
Today, we'll focus on **a very special case of the logarithm**, i.e., base **2**, which we sometimes call **the binary logarithm**. In essence, we'll focus on taking the powers of **2** and… Well, on second thought, why don't we dedicate [a whole section](https://www.omnicalculator.com/math/log-2#binary-logarithm) to this one?
## Binary logarithm
As mentioned at the end of [the above section](https://www.omnicalculator.com/math/log-2#what-is-a-logarithm), **the binary logarithm is a special case of the logarithmic function with base** **2**. That means that we'll have expressions of the form **log₂(x)**, and we'll ask ourselves to what power we should raise **2** in order to obtain **x**. For instance, we can easily observe that **log₂ 4 = 2**.
Seemingly, **2** is **a number like any other**. However, it has some interesting properties. E.g., it is the smallest prime number and the only even one. Moreover, it's the base for any computer-related operations via the binary representation.
Since it's so important, let's recall **a few basic powers of** **2**. Remember that the exponent can also be **0** or even negative.
| | | | | | | | | | | | | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| x | \-3 | \-2 | \-1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 2x | ⅛ | ¼ | ½ | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 |
Now we can see **some more examples** than just the **log₂ 4 = 2** from above. For instance, we can say that the log with base **2** of **8** is **3**. Similarly, **log₂ 16 = 4** or **log₂ 32 = 5**.
**But what is, say, log₂ 5?** Surely, **5** is not a power of **2**.
To be precise, **it's not an integer power of** **2**. We have to remember that there are also fractional exponents, and indeed, here, we need one of those. Unfortunately, **they're not so simple to guess**. In some cases, we can try to use tricks like the change of base rule, but, in general, it's best to use an external tool — something like our **log base 2 calculator** or the [change of base formula calculator](https://www.omnicalculator.com/math/change-of-base).
In it, you can see **two variable windows**: **x** and **log₂(x)**. Hopefully, the notation is self-explanatory. For example, if you'd like to find **log₂ 16**, you need to input **16** under **x**, and the calculator will give you the answer in the other window. If you require **log₂ 32**, you enter **32**. Also, note how Omni's log base 2 calculator **works both ways**: you can either input the value of **x** and obtain **log₂(x)** or the other way round.
**That'll be enough for today's lesson.** Go, my young padawan, and make sure to play around with the calculator or any other algebra-related tool that we have on offer.
## FAQs
### How do I calculate the logarithm in base 2?
To calculate the logarithm in base 2, you probably need a calculator. However, if you know the result of the natural logarithm or the base 10 logarithm of the same argument, you can follow these easy steps to find the result. For a number `x`:
1. Find the result of either `log10(x)` or `ln(x)`.
2. **Divide** the result of the previous step by the corresponding value between:
- `log10(2) = 0.30103`; or
- `ln(2) = 0.693147`.
3. The result of the division is `log2(x)`.
### What is the logarithm in base 2 of 256?
The logarithm in base 2 of **256** is **8**. To find this result, consider the following formula:
**2x = 256**
The logarithm corresponds to the following equation:
**log2(256) = x**
In this case, we can check the powers of 2 to see if we can find the value of **x**: **20 = 1**, **21 = 2**, **22 = 4**, …, **27 = 128**, and **28 = 256**.
Since we found the argument of our logarithm, we can write that:
**log2(256) = 8**.
### Why is the logarithm in base 2 important?
In a computer world, binary code is of essential importance: words, numbers, pictures, and everything else can be reduced to a string of 0s and 1s. Since the binary code uses only **two digits**, the number 2 appears consistently in computer science.
The widespread appearance of log2 in computer science has no strong mathematical reason (since logarithms can change base by multiplication) but can be useful. For example, using log2 to compute entropy allows us to obtain the result expressed in bits, which are the natural unit.
### What is the difference between ln and log2?
The difference between ln and log2 is the **base**. The logarithm is the **inverse operation of exponentiation**, that is, the power of a number, and it answers the question: "what is the exponent that produces a given result?".
The base of the logarithm is the number to which you apply the exponent: in the case of ln, the number is **e**, Neper's number. For log2, you must consider the number **2**. To sum up:
- If **b = ln(x)**, then **eb = x**; and
- If **c = log2(x)**, then **2c = x**.
### Related calculators
- [Exponential Function Calculator](https://www.omnicalculator.com/math/exponential-function)
x
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| Readable Markdown | Table of contents
- [What is a logarithm?](https://www.omnicalculator.com/math/log-2#what-is-a-logarithm)
- [Binary logarithm](https://www.omnicalculator.com/math/log-2#binary-logarithm)
- [FAQs](https://www.omnicalculator.com/math/log-2#faqs)
Welcome to Omni's **log base 2 calculator**. Your favorite tool to calculate the value of **log₂(x)** for arbitrary (positive) **x**. The operation is a special case of the logarithm, i.e., when the log's base is equal to **2**. As such, we sometimes call it **the binary logarithm**. If you wish to discover the more general case or know about the log rules, check out our [log calculator](https://www.omnicalculator.com/math/log) and our article "[Log Rules Made Simple: Understanding the Laws of Logarithms](https://www.omnicalculator.com/log-rules)".
So what is, e.g., the log with base **2** of **8**? Or **log₂ 16**? Or **log₂ 32**? Well, let's jump straight into the article and find out\!
## What is a logarithm?
As soon as humanity learned to add numbers, it found a way to simplify the notation for **adding the same number** several times: multiplication.
**5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 8 × 5**
Then, an obvious question appeared: how could we write **multiplying the same number** several times? And again, there came some smart mathematicians who introduced exponents.
**5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = 5⁸**
However, there is always that **one curious person** who asks the wildest questions. In this case, they wondered if there was a way to **invert all these operations**. Lucky for us, mathematics, and the whole world of science, other curious people found the answer.
For addition, it was easy: the inverse operation is **subtraction**. For multiplication, it's still pretty simple: it's division. For exponents, however, the story gets **more complicated**. After all, we know that **5 + 8 = 8 + 5** and **5 × 8 = 8 × 5**, but **5⁸** is very different from **8⁵**. So what should the inverse operation give? If we have **5⁸**, should it return **5** or **8**?
**The logarithm** (of base **5**) would be the operation if we chose option **8**. In other words, it is **a function that tells you the exponent needed to obtain the value**. Symbolically, we can write the definition like so:
💡 **logₐ(b)** gives you the power to which you'd need to raise **a** in order to obtain **b**. Note, however, that, in general, this can be a fractional exponent\!
For comparison, the inverse operation that would return the **5** from **5⁸** would be simply the (**8**\-th) root. If we wanted to get **a bit more technical**, then we could say that, in general, if we had an expression **xʸ**, then the root is the inverse operation for **x**, while the logarithm is that for **y**. And if we wanted to get **even more technical**, we'd say that the first inverts a polynomial function, while the latter inverts an exponential one.
Before we move further, let us have a pretty bullet list with **a few vital points of information about our new friend, the logarithm function**.
- There are **two very special cases of the logarithm** which have unique notation: [the natural logarithm](https://www.omnicalculator.com/math/natural-log) and the logarithm with base **10**. We denote them **ln(x)** and **log(x)** (the second one simply without the small **10**), and their bases are, respectively, the Euler number **e** and (surprise, surprise!) the number **10**.
*While the latter is obvious, the former may pose some problems – if you're not sure what the number **e** is, check out our [e calculator](https://www.omnicalculator.com/math/e-power-x).*
- **The logarithm function is defined only for positive numbers.** In other words, whenever we write **logₐ(b)**, we require **b** to be positive.
- Whatever the base, **the logarithm of** **1** **is equal to** **0**. After all, whatever we raise to power **0**, we get **1**. To learn how to change the base of your logarithm, access the article "[Change-of-base Formula Made Easy](https://www.omnicalculator.com/change-of-base-formula)".
- **Logarithms are extremely important.** And we mean **EXTREMELY** important. Outside of mathematics, they're used in **statistics** (e.g., the lognormal distribution), **economy** (e.g., the GDP index), **medicine** (e.g., the QUICKI index), and **chemistry** (e.g., the half-life decay). Also, quite **a few physical units** are based on logarithms, for instance, the Richter scale, the pH scale, and the dB scale.
Today, we'll focus on **a very special case of the logarithm**, i.e., base **2**, which we sometimes call **the binary logarithm**. In essence, we'll focus on taking the powers of **2** and… Well, on second thought, why don't we dedicate [a whole section](https://www.omnicalculator.com/math/log-2#binary-logarithm) to this one?
## Binary logarithm
As mentioned at the end of [the above section](https://www.omnicalculator.com/math/log-2#what-is-a-logarithm), **the binary logarithm is a special case of the logarithmic function with base** **2**. That means that we'll have expressions of the form **log₂(x)**, and we'll ask ourselves to what power we should raise **2** in order to obtain **x**. For instance, we can easily observe that **log₂ 4 = 2**.
Seemingly, **2** is **a number like any other**. However, it has some interesting properties. E.g., it is the smallest prime number and the only even one. Moreover, it's the base for any computer-related operations via the binary representation.
Since it's so important, let's recall **a few basic powers of** **2**. Remember that the exponent can also be **0** or even negative.
| | | | | | | | | | | | | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| x | \-3 | \-2 | \-1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 2x | ⅛ | ¼ | ½ | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 |
Now we can see **some more examples** than just the **log₂ 4 = 2** from above. For instance, we can say that the log with base **2** of **8** is **3**. Similarly, **log₂ 16 = 4** or **log₂ 32 = 5**.
**But what is, say, log₂ 5?** Surely, **5** is not a power of **2**.
To be precise, **it's not an integer power of** **2**. We have to remember that there are also fractional exponents, and indeed, here, we need one of those. Unfortunately, **they're not so simple to guess**. In some cases, we can try to use tricks like the change of base rule, but, in general, it's best to use an external tool — something like our **log base 2 calculator** or the [change of base formula calculator](https://www.omnicalculator.com/math/change-of-base).
In it, you can see **two variable windows**: **x** and **log₂(x)**. Hopefully, the notation is self-explanatory. For example, if you'd like to find **log₂ 16**, you need to input **16** under **x**, and the calculator will give you the answer in the other window. If you require **log₂ 32**, you enter **32**. Also, note how Omni's log base 2 calculator **works both ways**: you can either input the value of **x** and obtain **log₂(x)** or the other way round.
**That'll be enough for today's lesson.** Go, my young padawan, and make sure to play around with the calculator or any other algebra-related tool that we have on offer.
## FAQs
### How do I calculate the logarithm in base 2?
To calculate the logarithm in base 2, you probably need a calculator. However, if you know the result of the natural logarithm or the base 10 logarithm of the same argument, you can follow these easy steps to find the result. For a number `x`:
1. Find the result of either `log10(x)` or `ln(x)`.
2. **Divide** the result of the previous step by the corresponding value between:
- `log10(2) = 0.30103`; or
- `ln(2) = 0.693147`.
3. The result of the division is `log2(x)`.
### What is the logarithm in base 2 of 256?
The logarithm in base 2 of **256** is **8**. To find this result, consider the following formula:
**2x = 256**
The logarithm corresponds to the following equation:
**log2(256) = x**
In this case, we can check the powers of 2 to see if we can find the value of **x**: **20 = 1**, **21 = 2**, **22 = 4**, …, **27 = 128**, and **28 = 256**.
Since we found the argument of our logarithm, we can write that:
**log2(256) = 8**.
### Why is the logarithm in base 2 important?
In a computer world, binary code is of essential importance: words, numbers, pictures, and everything else can be reduced to a string of 0s and 1s. Since the binary code uses only **two digits**, the number 2 appears consistently in computer science.
The widespread appearance of log2 in computer science has no strong mathematical reason (since logarithms can change base by multiplication) but can be useful. For example, using log2 to compute entropy allows us to obtain the result expressed in bits, which are the natural unit.
### What is the difference between ln and log2?
The difference between ln and log2 is the **base**. The logarithm is the **inverse operation of exponentiation**, that is, the power of a number, and it answers the question: "what is the exponent that produces a given result?".
The base of the logarithm is the number to which you apply the exponent: in the case of ln, the number is **e**, Neper's number. For log2, you must consider the number **2**. To sum up:
- If **b = ln(x)**, then **eb = x**; and
- If **c = log2(x)**, then **2c = x**. | |||||||||||||||
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