Natural (ln) Log Calculator

Here is the answer to questions like: What is the natural log of 2? or How to find the natural log of 2?

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

What is natural logarithm?

The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. Natural logarithm is particular case of logarithms and is typically used in solving time, 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 log_ex.

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 e^{2.30258509...} = 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	log_en	n	log_en	n	log_en	n	log_en
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	log_en	n	log_en	n	log_en	n	log_en
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