Logarithm Calculator — Custom Base, Natural Log, Common Log &
Calculate logarithms in any custom base with the change of base formula explained step-by-step. Free, instant, and accurate.
Log Calculator
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Exponential Form
2^3 = 8
log₁₀(x)
0.903089987
ln(x)
2.079441542
log₂(x)
3
Change of Base
log_2(8) = log₁₀(8) / log₁₀(2) = 0.903089987 / 0.3010299957 = 3
Scenario Comparison
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log_2(8)
3
Logarithmic Curve f(x) = log2(x)
Step-by-Step Calculation
Exponential Form
2^3 = 8
Change of Base Formula
log_2(8) = log₁₀(8) / log₁₀(2) = 0.903089987 / 0.3010299957 = 3
Use this formula when your calculator only has log₁₀ or ln buttons.
log₁₀
0.903089987
ln (base e)
2.079441542
log₂
3
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