Logarithm & Inverse Logarithm
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# Logarithm and Anti-Log Calculator

getcalc.com's Logarithm and Inverse Log Calculator is an online basic math function tool to find the natural, base-2 or base-10 logarithm or anti-logarithm for a given number. Below is the solved example problem with steps to find logarithm functions for any number.
Steps to find logarithm

## Logarithm

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 logb 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
OperationFormulaExample
Multilicationlogb(x*y) = logb x + logb ylog5(75) = log5(3 * 25) = log5(3) + log5(25)
Divisionlogb(x/y) = logb(x) - logb(y)log2(1/4) = log2(1) - log2(4) = 0 - 2 = -2
Powerlogb(xy) = y * logb(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
100.13750.2630.37850.48540.5850.67810.76550.8480.926
211.07041.13751.20161.2631.32191.37851.4331.48541.5361
31.5851.63231.67811.72251.76551.80741.8481.88751.9261.9635
422.03562.07042.10432.13752.16992.20162.23272.2632.2928
52.32192.35052.37852.4062.4332.45942.48542.5112.53612.5607
62.5852.60882.63232.65542.67812.70042.72252.74422.76552.7866
72.80742.82782.8482.86792.88752.90692.9262.94492.96352.9819
833.01793.03563.05313.07043.08753.10433.1213.13753.1538
93.16993.18593.20163.21723.23273.24793.2633.2783.29283.3074
103.32193.33633.35053.36463.37853.39233.4063.41953.4333.4463
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
100.04140.07920.11390.14610.17610.20410.23040.25530.2788
20.3010.32220.34240.36170.38020.39790.4150.43140.44720.4624
30.47710.49140.50510.51850.53150.54410.55630.56820.57980.5911
40.60210.61280.62320.63350.64350.65320.66280.67210.68120.6902
50.6990.70760.7160.72430.73240.74040.74820.75590.76340.7709
60.77820.78530.79240.79930.80620.81290.81950.82610.83250.8388
70.84510.85130.85730.86330.86920.87510.88080.88650.89210.8976
80.90310.90850.91380.91910.92430.92940.93450.93950.94450.9494
90.95420.9590.96380.96850.97310.97770.98230.98680.99120.9956
1011.00431.00861.01281.0171.02121.02531.02941.03341.0374

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:
logb(x) = y, if by = 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

## Inverse Logarithm

Anti-log or inverse logarithm function is also a basic math function used to find the value of exponential function. In mathematics, an inverse log of 3 to the base 10 mathematically represented by 10y = x.

Solved Example Problem for Inverse Logarithm The below solved example problem may help you understand the mathematical function of anti-log or inverse logarithm. Use this antilog calculator to generate steps to find inverse logarithm for any given number.

Example Problem :
antilog2(6) = ?
What is antilog (base 10) of 4?
Workout :
step 1 Address the formula input parameters and values
Formula:
logb(x) = y, if by = x log10x = 4
y = 4
b = 10

step 2 Find the antilog value as per the formula
From the above formula
104 = x
x = 10000
log10(10000) = 4 