Logarithm and Inverse Log Calculator

Logarithm is a basic math function used to find how many times log base should be multiplied to produce a given number. Logarithm of x to base b equals to y can be mathematically described as log_b x = y which defines that the base "b" multiplied "y" times to produce a given number "x".

The below is some of the arithmetic rules and properties of logarithm function for multiplication, division, power and root.

Log and Anti-Log Formula
Operation	Formula	Example
Multilication	log_b(x*y) = log_b x + log_b y	log₅(75) = log₅(3 * 25) = log₅(3) + log₅(25)
Division	log_b(x/y) = log_b(x) - log_b(y)	log₂(1/4) = log₂(1) - log₂(4) = 0 - 2 = -2
Power	log_b(x^y) = y * log_b(x)	log₂(2⁴) = 4 * log₂(2) = 4

Logarithm Table for Base 2
#	.0	.1	.2	.3	.4	.5	.6	.7	.8	.9
0	-∞	-3.3219	-2.3219	-1.737	-1.3219	-1	-0.737	-0.5146	-0.3219	-0.152
1	0	0.1375	0.263	0.3785	0.4854	0.585	0.6781	0.7655	0.848	0.926
2	1	1.0704	1.1375	1.2016	1.263	1.3219	1.3785	1.433	1.4854	1.5361
3	1.585	1.6323	1.6781	1.7225	1.7655	1.8074	1.848	1.8875	1.926	1.9635
4	2	2.0356	2.0704	2.1043	2.1375	2.1699	2.2016	2.2327	2.263	2.2928
5	2.3219	2.3505	2.3785	2.406	2.433	2.4594	2.4854	2.511	2.5361	2.5607
6	2.585	2.6088	2.6323	2.6554	2.6781	2.7004	2.7225	2.7442	2.7655	2.7866
7	2.8074	2.8278	2.848	2.8679	2.8875	2.9069	2.926	2.9449	2.9635	2.9819
8	3	3.0179	3.0356	3.0531	3.0704	3.0875	3.1043	3.121	3.1375	3.1538
9	3.1699	3.1859	3.2016	3.2172	3.2327	3.2479	3.263	3.278	3.2928	3.3074
10	3.3219	3.3363	3.3505	3.3646	3.3785	3.3923	3.406	3.4195	3.433	3.4463

Logarithm Table for Base 10
#	.0	.1	.2	.3	.4	.5	.6	.7	.8	.9
0	-∞	-1	-0.699	-0.5229	-0.3979	-0.301	-0.2218	-0.1549	-0.0969	-0.0458
1	0	0.0414	0.0792	0.1139	0.1461	0.1761	0.2041	0.2304	0.2553	0.2788
2	0.301	0.3222	0.3424	0.3617	0.3802	0.3979	0.415	0.4314	0.4472	0.4624
3	0.4771	0.4914	0.5051	0.5185	0.5315	0.5441	0.5563	0.5682	0.5798	0.5911
4	0.6021	0.6128	0.6232	0.6335	0.6435	0.6532	0.6628	0.6721	0.6812	0.6902
5	0.699	0.7076	0.716	0.7243	0.7324	0.7404	0.7482	0.7559	0.7634	0.7709
6	0.7782	0.7853	0.7924	0.7993	0.8062	0.8129	0.8195	0.8261	0.8325	0.8388
7	0.8451	0.8513	0.8573	0.8633	0.8692	0.8751	0.8808	0.8865	0.8921	0.8976
8	0.9031	0.9085	0.9138	0.9191	0.9243	0.9294	0.9345	0.9395	0.9445	0.9494
9	0.9542	0.959	0.9638	0.9685	0.9731	0.9777	0.9823	0.9868	0.9912	0.9956
10	1	1.0043	1.0086	1.0128	1.017	1.0212	1.0253	1.0294	1.0334	1.0374

Solved Example Problem for Logarithm
The below solved example problem may help you understand the mathematical function of logarithm. Use this logarithm calculator to generate steps to find base-2, base-10 or natural logarithm for any given number.
Example Problem:
log₂(1/64) = ?
What is log base 2 of 1/64?
Workout :
step 1 Address the formula, input parameters and values
Formula:
log_b(x) = y, if b^y = x
x = 1/64
b = 2
log₂(1/64) = y

step 2 Write the number 1/64 in raising 2 to the nth power
(2)^y = 1/64
1/64 = 1/2⁶
1/64 = 2^-6
(2)^y = 2^-6
y = -6
log₂(1/64) = -6

Logarithm and Anti-Log Calculator

Logarithm

Inverse Logarithm