Log Calculator

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Logarithm Calculator

Calculate the logarithm of a positive number for any valid real base and verify the result with an exponent check.

Last updated: June 2026 | By Patchworkr Team

Log Solver
log base b of x
2
10^2 = 100
Input
100
Base
10
Check
10^2 = 100

What Is a Logarithm?

A logarithm answers the question "what power do I raise the base to in order to get the value?" For a valid base b and value x, log base b of x is the exponent y such that b^y = x.

How to Calculate a Logarithm

  1. Enter a positive value x.
  2. Enter a base b greater than 0 and not equal to 1.
  3. Compute y = ln(x) / ln(b).
  4. Verify the result by checking that b^y = x.
log_b(x) = ln(x) / ln(b)

Worked Example

For x = 100 and b = 10, the result is 2.

log10(100) = 2

Frequently Asked Questions

Why is the base restricted?

The base must be positive and not equal to 1 so the logarithm is well-defined and not degenerate.

Can the input be less than 1?

Yes. The result is negative whenever the value is between 0 and 1.

Does the tool accept decimals?

Yes. Any finite real value and valid base are accepted, including scientific notation.

What if the value is blank?

Blank input is treated as invalid instead of being silently converted to zero.

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