Calculate logarithm

Calculate a logarithm in a chosen base, its natural and base-10 forms, and the matching inverse power.

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ToolLogarithm Calculator
Input
Output
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How it works

The change-of-base identity log_b(x) = ln(x) ÷ ln(b) computes the requested base from natural logarithms. The inverse raises the selected base to the supplied exponent, and the result also includes base-10 and natural-log values.

  • Base 10 is the initial choice because common logarithms are familiar in measurement tables.
  • Results are rounded to a fixed display precision.

Worked example

log base 2 of 8
A clean power of two, so the change of base working comes out exact
Input
											Value: 8
Base: 2
Output
												Log base: 3
Natural log: 2.079442
Log10: 0.90309
Antilog base: 256
Change of base working: log base 2 of 8 = ln(8) / ln(2) = 2.079442 / 0.693147 = 3

When to use this

pH and decibel work uses logarithmic scales, growth models solve for exponents, and computer-science lessons compare binary and decimal logarithms.

Edge cases

  • A value of zero or below has no real logarithm and is rejected.
  • Base one is rejected because ln(1) is zero and cannot form the denominator.
  • A fractional exponent can produce a valid inverse result even though the input is not an integer.

References