Natural (ln) Log Calculator
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(5 ∙ 3) = 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) = 5∙ ln(3) |
ln of reciprocal |
ln(1/x) = −ln(x) | |
ln of negative number |
ln(x) is undefined when x ≤ 0 | |
ln of e |
ln(e) = 1 | |
ln of zero |
ln(0) is undefined | |
ln of one |
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 |
Natural (ln) Log Calculator
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Sample Natural Log Calculations
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