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Math / Log

Log Calculator

Evaluate log base b of a positive number x, answering the question b raised to what power gives x. The base is checked against the logarithm’s domain, and the change-of-base relation is shown for verification. log_b(x)=ln(x)/ln(b), requiring x>0, b>0, and b≠1. The logarithm is the inverse of exponentiation: its answer y must satisfy b^y=x. The change-of-base relation permits any valid base to be evaluated with natural logarithms.

Your inputs

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Calculator settings

Your result
5
log base 2
Check
2^result = 32

Example inputs shown. Adjust them to explore.

A familiar situation

Solve a simple exponential equation by finding the logarithm of its positive argument.

How to use this calculator

  1. Enter base, positive argument.
  2. Select Calculate to see the answer and its breakdown.
  3. Keep a scenario, change an input and compare the results.

Use consistent units and check the assumptions below before applying the result.

How log is calculated

log_b(x)=ln(x)/ln(b), requiring x>0, b>0, and b≠1. The logarithm is the inverse of exponentiation: its answer y must satisfy b^y=x. The change-of-base relation permits any valid base to be evaluated with natural logarithms. log₂(32)=5 because 2⁵=32.

log_b(x)=ln(x)/ln(b), where x>0, b>0, b≠1.
A worked example

log₂(32)=5 because 2⁵=32.

Assumptions & useful context

The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.

Frequently asked questions

Can the base be 1?

No; powers of 1 never distinguish positive inputs.

Can the input be zero or negative?

Real logarithms are defined only for positive arguments.

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