# Natural (ln) Log Calculator

### Natural Logarithm Calculator - ln(x)

 Please enter a positive number (x) to calculate ln(x): ln(  ) = ? Result: The natural logarithm of 40 is 3.6888794541139 or ln(40) = 3.6888794541139. Notes: i) e and pi are accepted values. ii) 1.2 x 103 should be entered as 1.2e3 and iii) 1.2 x 10-3 as 1.2e-3

Here is the answer to questions like: What is the natural log of 40? Or How do you find the natural log of 40?

Use our base e-log calculator to find the natural logarithm of any positive real number.

## What is a natural logarithm?

The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. It is a particular case of logarithms and is typically used in solving time and growth/decay problems.

The number 'e' is an irrational constant approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln(x) or logex.

The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln(10) is 2.30258509..., because e2.30258509... = 10.

## Natural Logarithm Basic Rules

Rule name Rule Example

### Product rule

ln(x ∙ y) = ln(x) + ln(y)

ln(53) = ln(5) + ln(3)

### Quotient rule

ln(x / y) = ln(x) - ln(y)

ln(5 / 3) = ln(5) - ln(3)

### Power rule

ln(x y) = y ∙ ln(x)

ln(35) = 5ln(3)

### ln of reciprocal

ln(1/x) = −ln(x)

### ln of negative number

ln(x) is undefined when x ≤ 0

ln(e) = 1

### ln of zero

ln(0) is undefined

ln(1) = 0

### ln of infinity

lim ln(x) = ∞ ,when x→∞

### ln derivative

[ln(x)]' = 1 / x

### ln integral

ln(x)dx = x ∙ (ln(x) - 1) + C

## The natural logarithm table (<= 1.0)

n logen n logen n logen n logen
0.01 -4.60517 0.26 -1.34707 0.51 -0.67334 0.76 -0.27443
0.02 -3.91202 0.27 -1.30933 0.52 -0.65392 0.77 -0.26136
0.03 -3.50655 0.28 -1.27296 0.53 -0.63488 0.78 -0.24846
0.04 -3.21887 0.29 -1.23788 0.54 -0.61618 0.79 -0.23572
0.05 -2.99573 0.30 -1.20397 0.55 -0.59783 0.80 -0.22314
0.06 -2.81341 0.31 -1.17118 0.56 -0.57982 0.81 -0.21072
0.07 -2.65926 0.32 -1.13943 0.57 -0.56212 0.82 -0.19845
0.08 -2.52573 0.33 -1.10866 0.58 -0.54472 0.83 -0.18633
0.09 -2.40794 0.34 -1.07881 0.59 -0.52763 0.84 -0.17435
0.10 -2.30258 0.35 -1.04982 0.60 -0.51082 0.85 -0.16252
0.11 -2.20727 0.36 -1.02165 0.61 -0.49430 0.86 -0.15082
0.12 -2.12026 0.37 -0.99425 0.62 -0.47803 0.87 -0.13926
0.13 -2.04022 0.38 -0.96758 0.63 -0.46203 0.88 -0.12783
0.14 -1.96611 0.39 -0.94161 0.64 -0.44629 0.89 -0.11653
0.15 -1.89712 0.40 -0.91629 0.65 -0.43078 0.90 -0.10536
0.16 -1.83258 0.41 -0.89160 0.66 -0.41551 0.91 -0.09431
0.17 -1.77196 0.42 -0.86750 0.67 -0.40047 0.92 -0.08338
0.18 -1.71480 0.43 -0.81419 0.68 -0.38566 0.93 -0.07257
0.19 -1.66073 0.44 -0.82098 0.69 -0.37106 0.94 -0.06187
0.20 -1.60944 0.45 -0.79851 0.70 -0.35667 0.95 -0.05129
0.21 -1.56065 0.46 -0.77653 0.71 -0.34249 0.96 -0.04082
0.22 -1.51412 0.47 -0.75502 0.72 -0.32850 0.97 -0.03046
0.23 -1.46968 0.48 -0.73397 0.73 -0.31471 0.98 -0.02020
0.24 -1.42711 0.49 -0.71335 0.74 -0.30110 0.99 -0.01005
0.25 -1.38629 0.50 -0.69214 0.75 -0.28768 1.00 -0.00000

## The natural logarithm table (>= 1.0)

n logen n logen n logen n logen
1.0 0.00000 3.0 1.09861 5.0 1.60944 25.0 3.21887
1.1 0.09531 3.1 1.13140 6.0 1.79176 26.0 3.25809
1.2 0.18232 3.2 1.16315 7.0 1.94591 27.0 3.29583
1.3 0.26236 3.3 1.19392 8.0 2.07944 28.0 3.33220
1.4 0.33647 3.4 1.22377 9.0 2.19722 29.0 3.36729
1.5 0.40546 3.5 1.25276 10.0 2.30258 30.0 3.40119
1.6 0.47000 3.6 1.28093 11.0 2.39789 40.0 3.68888
1.7 0.53063 3.7 1.30833 12.0 2.48491 50.0 3.91202
1.8 0.58779 3.8 1.33500 13.0 2.56495 60.0 4.09434
1.9 0.64185 3.9 1.36097 14.0 2.63905 70.0 4.24849
2.0 0.69314 4.0 1.38629 15.0 2.70805 80.0 4.38202
2.1 0.74193 4.1 1.41099 16.0 2.77259 90.0 4.49981
2.2 0.78845 4.2 1.43508 17.0 2.83321 100.0 4.60517
2.3 0.83291 4.3 1.45861 18.0 2.89037 200.0 5.29832
2.4 0.87547 4.4 1.48160 19.0 2.94444 300.0 5.70378
2.5 0.91629 4.5 1.50408 20.0 2.99573 400.0 5.99146
2.6 0.95551 4.6 1.52605 21,0 3.04452 500.0 6.21461
2.7 0.99325 4.7 1.54756 22,0 3.09104 600.0 6.39693
2.8 1.02962 4.8 1.56861 23.0 3.13549 700.0 6.55108
2.9 1.06471 4.9 1.58923 24.0 3.17805 800.0 6.68461