← All algebra calculators

ALGEBRA / EXPONENTIALS & LOGARITHMS

Exponential and Logarithmic Equation Solver with Domain Checks and Step-by-Step Results

Updated By Unit Conversion Plus

Solve common exponential and logarithmic equations and check the restrictions that make the logarithms valid.

Choose an equation form

Solving exponential equations

When an exponential equation has one exponential expression, take logarithms of both sides and use the power rule to bring the exponent down. If both sides use the same valid base, their exponents can be equated directly.

Solving logarithmic equations

Rewrite log base a of y equals c as y = a^c. A logarithm requires a positive argument, a positive base and a base other than 1. Every proposed solution must satisfy those conditions.

Exact form and decimal form

The calculator displays the logarithmic formula used to isolate x as well as a decimal approximation. Rounding happens only in the displayed decimal; the verification uses the calculated value before display rounding.

Frequently asked questions

Why must a logarithm’s argument be positive?

A real logarithm answers which real exponent produces the argument from a positive base, and positive bases raised to real powers remain positive.

Can the exponential base equal 1?

No. A base of 1 produces the constant value 1 and does not define an invertible exponential or logarithmic function.