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Logarithm Calculator.

Calculate a logarithm for any valid positive base and argument.

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01

Set your values

Results update as you type.

Greater than 0 and not 1

Presets

How to Use

A logarithm answers the question: what exponent on the base gives the argument? For example, log₂(8) = 3 because 2³ = 8.

For a real logarithm, the argument must be greater than 0, and the base must be greater than 0 but not equal to 1. Bases between 0 and 1 are valid and produce a decreasing logarithm.

FAQs

What is a logarithm?

A logarithm is the exponent needed to raise a base to a given positive argument. For example, log₂(8) = 3 because 2³ = 8.

Which bases are valid?

For real logarithms, the base must be positive and different from 1, and the argument must be greater than 0.

Cite this calculator

Canonical URL: https://mathify.one/en/math/logarithm

Cite as: Mathify. (2026). Logarithm Calculator. https://mathify.one/en/math/logarithm

Use Cases

Solve math homework problems

Quickly find logarithms with any base for algebra or precalculus assignments, with step-by-step working to verify your own calculations.

Example: Find log base 2 of 8: enter base 2 and number 8 to get 3.

Check scientific or engineering calculations

Use the calculator to verify logarithms in fields like computer science (log base 2), acoustics (decibels), or chemistry (pH), ensuring accuracy.

Example: Compute log base 10 of 1000 to confirm a pH-related value.

Frequently Asked Questions

How does the Logarithm Calculator work?
It uses the change-of-base formula: log_b(x) = log(x) / log(b). You input the base (b) and the number (x), and the calculator computes the logarithm, showing each step of the calculation.
What is the change-of-base formula?
The change-of-base formula allows you to compute logarithms with any base using common (base 10) or natural (base e) logarithms: log_b(x) = log_c(x) / log_c(b). This calculator uses it to provide results for any positive base and number.
Can I use this calculator for any base?
Yes, as long as the base is a positive number not equal to 1, and the number is positive. The calculator will handle any valid base, including fractions and decimals.

Tips & Common Mistakes

Tips

  • Ensure the base is a positive number greater than 0 and not equal to 1, otherwise the logarithm is undefined.
  • The number (argument) must be positive; logarithms of zero or negative numbers are not real.
  • Use the step-by-step working to understand how the change-of-base formula is applied, which helps in learning.
  • For quick mental checks, remember common logs: log base 10 of 100 is 2, log base 2 of 32 is 5.

Common Mistakes to Avoid

  • Entering a base of 1, which is invalid because log base 1 is undefined.
  • Entering a negative number or zero as the argument, which does not produce a real logarithm.
  • Confusing the base and the argument, leading to incorrect results.

Last updated: August 13, 2026