Exponential & Log Equations

Solve equations with powers and logarithms, using matching bases, log laws and the change-of-base rule. Try “solve 3^(2x) = 81” or “log₂(x) + log₂(x − 2) = 3”.

Try an example:

What you can do with the Exponential & Log Equations

Solve equations with powers and logarithms.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. solve 3^(2x) = 81 and log2(x) + log2(x-2) = 3

How the Exponential & Log Equations works

  1. If possible, write both sides with the same base and equate the exponents.
  2. Otherwise take logs of both sides, or combine logs with the product and quotient laws.
  3. Solve for x and reject any answer that makes a log argument zero or negative.

Frequently asked questions

Why do I have to check log solutions?

The argument of a log must be positive. Some algebraic solutions make it negative and must be rejected.

What is the change-of-base formula?

log_b(x) = ln(x) ÷ ln(b), which lets you evaluate any log on a calculator.

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Math Solver can make mistakes. Please double-check important steps and calculations.