Logarithm Calculator

Calculate logarithms with any base, natural log (ln), and common log (log). View log graphs and reference tables.

Logarithm Properties

log_b(xy) = log_b(x) + log_b(y)
log_b(x/y) = log_b(x) - log_b(y)
log_b(x^n) = n · log_b(x)
log_a(x) = log_b(x) / log_b(a)
log_b(1) = 0, log_b(b) = 1

Logarithm Graph

05101520-4-2024

Common Logarithm Values

nlog₁₀(n)ln(n)log₂(n)
10.00000.00000.0000
20.30100.69311.0000
30.47711.09861.5850
40.60211.38632.0000
50.69901.60942.3219
60.77821.79182.5850
70.84511.94592.8074
80.90312.07943.0000
90.95422.19723.1699
101.00002.30263.3219
111.04142.39793.4594
121.07922.48493.5850
131.11392.56493.7004
141.14612.63913.8074
151.17612.70813.9069
161.20412.77264.0000
171.23042.83324.0875
181.25532.89044.1699
191.27882.94444.2479
201.30102.99574.3219

Logarithm Calculator FAQ

What is a logarithm?

A logarithm is the inverse of exponentiation. log_b(x) = y means b^y = x. For example, log_2(8) = 3 because 2³ = 8.

Difference between common log and natural log?

Common log (log) has base 10, natural log (ln) has base e (≈2.718). Common log is used in engineering, natural log in math and science.

What is the change of base formula?

log_a(x) = log_b(x) / log_b(a). This lets you convert between any two bases.

Logarithm Calculator Guide

The Logarithm Calculator computes common log (log), natural log (ln), and logarithms with any base. It also supports inverse operations (exponentiation) and provides graph visualization and reference tables for learning and engineering.

This calculator is provided for informational purposes only.

Results are estimates and may differ from actual amounts.

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