# Logarithm Calculator

Log calculator finds the logarithm function result (can be called exponent) from the given base number and a real number.

Log Calculator log
logb(x) = y

logb(x) = y
x = logb(bx)
logb(x) = y is equivalent to x = by

b: log base number, b>0 and b≠1
x: is real number, x>0

## Logarithm

Logarithm is considered to be one of the basic concepts in mathematics. There are plenty of definitions, starting from really complicated and ending up with rather simple ones. In order to answer a question, what a logarithm is, let's take a look at the table below:

 21 22 23 24 25 26 2 4 8 16 32 64

This is the table in which we can see the values of two squared, two cubed, and so on. This is an operation in mathematics, known as exponentiation. If we look at the numbers at the bottom line, we can try to find the power value to which 2 must be raised to get this number. For example, to get 16, it is necessary to raise two to the fourth power. And to get a 64, you need to raise two to the sixth power.

Therefore, logarithm is the exponent to which it is necessary to raise a fixed number (which is called the base), to get the number y. In other words, a logarithm can be represented as the following:

logb x = y

with b being the base, x being a real number, and y being an exponent.

For example, 23 = 8 ⇒ log2 8 = 3 (the logarithm of 8 to base 2 is equal to 3, because 23 = 8).
Similarly, log2 64 = 6, because 26 = 64.

Therefore, it is obvious that logarithm operation is an inverse one to exponentiation.

 21 22 23 24 25 26 2 4 8 16 32 64 log22 = 1 log24 = 2 log28 = 3 log216 = 4 log232 = 5 log264 = 6

Unfortunately, not all logarithms can be calculated that easily. For example, finding log2 5 is hardly possible by just using our simple calculation abilities. After using logarithm calculator, we can find out that

log2 5 = 2,32192809

There are a few specific types of logarithms. For example, the logarithm to base 2 is known as the binary logarithm, and it is widely used in computer science and programming languages. The logarithm to base 10 is usually referred to as the common logarithm, and it has a huge number of applications in engineering, scientific research, technology, etc. Finally, so called natural logarithm uses the number e (which is approximately equal to 2.71828) as its base, and this kind of logarithm has a great importance in mathematics, physics, and other precise sciences.

The logarithm logb(x) = y is read as log base b of x is equals to y.
Please note that the base of log number b must be greater than 0 and must not be equal to 1. And the number (x) which we are calculating log base of (b) must be a positive real number.

For example log 2 of 8 is equal to 3.

```log2(8) = 3 (log base 2 of 8)
The exponential is 23 = 8
```

### Common Values for Log Base

Log BaseLog NameNotationLog Example
2binary logarithmlb(x)log2(16) = lb(16) = 4 => 24 = 16
10common logarithmlg(x)log10(1000) = lg(1000) = 3 => 103 = 1000
enatural logarithmln(x)loge(8) = ln(8) = 2.0794 => e2.0794 = 8

### Logarithmic Identities

List of logarithmic identites, formulas and log examples in logarithm form.

#### Logarithm of a Product

```logb(x·y) = logb(x) + logb(y)
log2(5·7) = log2(5) + log2(7)```

#### Logarithm of a Quotient

```logb(x/y) = logb(x) - logb(y)
log2(5/7) = log2(5) - log2(7)```

#### Logarithm of a Power

```logb(xy) = y·logb(x)
log2(57) = 7·log2(5)```

#### Change of Base

```logb(x) = (logk(x)) / (logk(b))
```

#### Logarithm Values Tables

List of log function values tables in common base numbers.

Number (x)Notationlog2(x)
log2(1)lb(1)0
log2(2)lb(2)1
log2(3)lb(3)1.584963
log2(4)lb(4)2
log2(5)lb(5)2.321928
log2(6)lb(6)2.584963
log2(7)lb(7)2.807355
log2(8)lb(8)3
log2(9)lb(9)3.169925
log2(10)lb(10)3.321928
log2(11)lb(11)3.459432
log2(12)lb(12)3.584963
log2(13)lb(13)3.70044
log2(14)lb(14)3.807355
log2(15)lb(15)3.906891
log2(16)lb(16)4
log2(17)lb(17)4.087463
log2(18)lb(18)4.169925
log2(19)lb(19)4.247928
log2(20)lb(20)4.321928
log2(21)lb(21)4.392317
log2(22)lb(22)4.459432
log2(23)lb(23)4.523562
log2(24)lb(24)4.584963
log2(25)lb(25)4.643856
log2(26)lb(26)4.70044
log2(27)lb(27)4.754888
log2(28)lb(28)4.807355
log2(29)lb(29)4.857981
log2(30)lb(30)4.906891
log2(31)lb(31)4.954196
log2(32)lb(32)5
log2(33)lb(33)5.044394
log2(34)lb(34)5.087463
log2(35)lb(35)5.129283
log2(36)lb(36)5.169925
log2(37)lb(37)5.209453
log2(38)lb(38)5.247928
log2(39)lb(39)5.285402
log2(40)lb(40)5.321928
log2(41)lb(41)5.357552
log2(42)lb(42)5.392317
log2(43)lb(43)5.426265
log2(44)lb(44)5.459432
log2(45)lb(45)5.491853
log2(46)lb(46)5.523562
log2(47)lb(47)5.554589
log2(48)lb(48)5.584963
log2(49)lb(49)5.61471
log2(50)lb(50)5.643856
log2(51)lb(51)5.672425
log2(52)lb(52)5.70044
log2(53)lb(53)5.72792
log2(54)lb(54)5.754888
log2(55)lb(55)5.78136
log2(56)lb(56)5.807355
log2(57)lb(57)5.83289
log2(58)lb(58)5.857981
log2(59)lb(59)5.882643
log2(60)lb(60)5.906891
log2(61)lb(61)5.930737
log2(62)lb(62)5.954196
log2(63)lb(63)5.97728
log2(64)lb(64)6
Number (x)Notationlog10(x)
log10(1)log(1)0
log10(2)log(2)0.30103
log10(3)log(3)0.477121
log10(4)log(4)0.60206
log10(5)log(5)0.69897
log10(6)log(6)0.778151
log10(7)log(7)0.845098
log10(8)log(8)0.90309
log10(9)log(9)0.954243
log10(10)log(10)1
log10(11)log(11)1.041393
log10(12)log(12)1.079181
log10(13)log(13)1.113943
log10(14)log(14)1.146128
log10(15)log(15)1.176091
log10(16)log(16)1.20412
log10(17)log(17)1.230449
log10(18)log(18)1.255273
log10(19)log(19)1.278754
log10(20)log(20)1.30103
log10(21)log(21)1.322219
log10(22)log(22)1.342423
log10(23)log(23)1.361728
log10(24)log(24)1.380211
log10(25)log(25)1.39794
log10(26)log(26)1.414973
log10(27)log(27)1.431364
log10(28)log(28)1.447158
log10(29)log(29)1.462398
log10(30)log(30)1.477121
log10(31)log(31)1.491362
log10(32)log(32)1.50515
log10(33)log(33)1.518514
log10(34)log(34)1.531479
log10(35)log(35)1.544068
log10(36)log(36)1.556303
log10(37)log(37)1.568202
log10(38)log(38)1.579784
log10(39)log(39)1.591065
log10(40)log(40)1.60206
log10(41)log(41)1.612784
log10(42)log(42)1.623249
log10(43)log(43)1.633468
log10(44)log(44)1.643453
log10(45)log(45)1.653213
log10(46)log(46)1.662758
log10(47)log(47)1.672098
log10(48)log(48)1.681241
log10(49)log(49)1.690196
log10(50)log(50)1.69897
log10(51)log(51)1.70757
log10(52)log(52)1.716003
log10(53)log(53)1.724276
log10(54)log(54)1.732394
log10(55)log(55)1.740363
log10(56)log(56)1.748188
log10(57)log(57)1.755875
log10(58)log(58)1.763428
log10(59)log(59)1.770852
log10(60)log(60)1.778151
log10(61)log(61)1.78533
log10(62)log(62)1.792392
log10(63)log(63)1.799341
log10(64)log(64)1.80618
Number (x)Notationln(x)
loge(1)ln(1)0
loge(2)ln(2)0.693147
loge(3)ln(3)1.098612
loge(4)ln(4)1.386294
loge(5)ln(5)1.609438
loge(6)ln(6)1.791759
loge(7)ln(7)1.94591
loge(8)ln(8)2.079442
loge(9)ln(9)2.197225
loge(10)ln(10)2.302585
loge(11)ln(11)2.397895
loge(12)ln(12)2.484907
loge(13)ln(13)2.564949
loge(14)ln(14)2.639057
loge(15)ln(15)2.70805
loge(16)ln(16)2.772589
loge(17)ln(17)2.833213
loge(18)ln(18)2.890372
loge(19)ln(19)2.944439
loge(20)ln(20)2.995732
loge(21)ln(21)3.044522
loge(22)ln(22)3.091042
loge(23)ln(23)3.135494
loge(24)ln(24)3.178054
loge(25)ln(25)3.218876
loge(26)ln(26)3.258097
loge(27)ln(27)3.295837
loge(28)ln(28)3.332205
loge(29)ln(29)3.367296
loge(30)ln(30)3.401197
loge(31)ln(31)3.433987
loge(32)ln(32)3.465736
loge(33)ln(33)3.496508
loge(34)ln(34)3.526361
loge(35)ln(35)3.555348
loge(36)ln(36)3.583519
loge(37)ln(37)3.610918
loge(38)ln(38)3.637586
loge(39)ln(39)3.663562
loge(40)ln(40)3.688879
loge(41)ln(41)3.713572
loge(42)ln(42)3.73767
loge(43)ln(43)3.7612
loge(44)ln(44)3.78419
loge(45)ln(45)3.806662
loge(46)ln(46)3.828641
loge(47)ln(47)3.850148
loge(48)ln(48)3.871201
loge(49)ln(49)3.89182
loge(50)ln(50)3.912023
loge(51)ln(51)3.931826
loge(52)ln(52)3.951244
loge(53)ln(53)3.970292
loge(54)ln(54)3.988984
loge(55)ln(55)4.007333
loge(56)ln(56)4.025352
loge(57)ln(57)4.043051
loge(58)ln(58)4.060443
loge(59)ln(59)4.077537
loge(60)ln(60)4.094345
loge(61)ln(61)4.110874
loge(62)ln(62)4.127134
loge(63)ln(63)4.143135
loge(64)ln(64)4.158883

Husam 2019-10-10 00:53:16

Please solve log2 base x + 48logx base 2=14

akash 2019-10-06 07:51:18

find the value log1(2) or log1(1)

Guest 2019-10-02 09:04:11

What is the value of log(1/2)¹²

Guest 2019-10-02 05:59:27

Please solve log a base x + log e base x^6 please it is of differentiation

Jijakalidas 2019-09-27 02:09:14

How to solve log base3 56

Hasarel 2019-09-20 18:32:02

Thanks for giving us such facilities

SINKONDE 2019-09-13 11:20:20

Please can you solve this equation?
Logp y=0.2356,solve log p|y

Guest 2019-09-10 11:36:39

loga+logb+logc+logd=100 abcd

queen Leah 2019-08-24 16:20:06

Pls help with this question and I need the solution now pls:3/2 Log 27-3 Log 5 into square root of 5 divided by Log 0.4

Jose 2019-08-23 21:59:45

y = log(8 + x/10) x=5.0 need help salving for Y=

Prity 2019-07-29 05:45:17

It is good for students

gimesha 2019-07-21 18:00:50

How to calculate 1/2 log c-1/2 log c/10 step by step

Jayesh Kshirsagar 2019-07-14 10:55:35

1/2 log (10^-2)

anaya 2019-06-14 01:23:26

2 log base10 2-1.2 kidly solve it step by step

Rufaro Tsambarikagwa 2019-05-19 14:09:56

logs are difficult to solve bt through the use of this site l have been helped a lot s

salawu illias 2019-05-16 09:36:43

pls wat is answer for 23 log10raise to power of 3

azka 2019-05-10 07:49:16

36 log 0,2

sushant 2019-05-08 03:01:20

value of log1/13

kaveh 2019-04-30 22:59:11

log[2](3)=a
log[5](9)=b
log[40](6)=?
thank you

anonymous 2019-04-23 13:52:17

solve:
log12(20)=y-2

Johann 2019-04-23 09:14:53

Bitte um Hilfe !

log2 [3+log4 (5+log6 (x))]=2

BOSTON 2019-04-16 11:44:44

Use fact that log2base10 and x=4,find the value of log10base x2.

tofu 2019-04-12 22:33:57

log x square base 2 minus log x base 2 equals 3 solve x

ERIC tan 2019-03-28 06:24:04

how to solve : lg24*lgx^2=5lg12

chizzy 2019-03-25 12:28:01

help me out with this question.log2base4×log4base2

some guy 2019-03-22 10:34:46

log10(a) + log10(b) = 2
sqrt(a) + sqrt(b) = 8

Possible values of a and b?

Ravi 2019-03-16 08:08:41

Evaluate log27 base 3 + log8 base 2

Guest 2019-01-31 21:54:30

Logx+log15=log45

Hassan Omar 2019-01-31 21:53:32

Special math

Guest 2019-01-31 00:52:07

Logx+log15=log45

Guest 2019-01-23 01:10:28

Hey what is 7log2 - 1/2log16 +log3

Yonda 2019-01-17 03:19:07

solving for (log 3^3/2 - log 2^3/2)/ log3/2

My name is John 2019-01-12 09:55:37

PLEASE solve the following :(log27)(log36)/(log216)(log3). Without using log table.

Pretty 2019-01-06 16:10:33

Thanks

Lawrence Appiah-Nuamah 2018-12-28 00:07:22

Given 49 raised to the power log z to the base 7 = 2 . Find the variable

Value of Iog 1/5

Diamond 2018-10-28 09:54:48

krishna 2018-10-05 20:00:51

thanks

krishna 2018-10-05 20:00:51

thanks

Harper Li 2018-10-02 16:30:40

Can you please solve, with an explanation, "simplify the product (log(216,28))(log2,6) + log(√(7),6))".

Saavi 2018-10-02 04:45:38

Whtat is the value of log 2*pi

Mayowa 2018-09-20 15:10:01

Can u pls solve log 25 square of 3 +log 2 square root of 3 -log 7 square of 3

Om PRAKASH 2018-09-15 05:52:26

1/3log 64

Kim 2018-08-14 20:25:49

Never mind I figured it out. thank you any way
t= 11/2xlog10(0.7)/log10(1/2)

equals approximately 2.8 billion

Kim 2018-08-14 20:18:55

t = 11/2 x log10(0.7)/log10(1/2)

equals approximately 2.8billion How do you get this answer?

Carole Filyaw 2018-08-10 09:53:43

How to solve for

[1*10^-14]*[2*10^-8]

Reitumetse 2018-08-06 17:04:00

How to solve 20^log5/5^log2

Hannah 2018-07-15 23:55:10

How do you solve this?
Solve for x in terms of y and z:
61) 9^y=3^z/3^x
62) log[7](3)=y;log[7](2)=z;x=log[3](2)
63) y=log[a](9); x= log[a](3)
Thank you

Yipi :D 2018-06-11 11:04:09

Found it, X = 2,2255...

Yipi :D 2018-06-11 10:57:50

How can I solve (ln e exponent 2) x (ln x exponent 3) - ln x + 3 = 7 Please