Solving log equations

Math

Definition

Finding the value of the variable in equations that contain logarithms. Techniques include converting to exponential form, using logarithm properties to combine or expand logs, and checking for extraneous solutions (since log arguments must be positive).

How It Works

  1. Use logarithm properties to combine logs on each side into a single logarithm.
  2. Convert the logarithmic equation to exponential form.
  3. Solve the resulting equation for the variable.
  4. Check all solutions to ensure the arguments of every original logarithm are positive.

Examples

  • log₂(x) = 5 → x = 2⁵ = 32
  • log(x) + log(x−3) = 1 → log(x(x−3)) = 1 → x(x−3) = 10 → x = 5 (x = −2 is extraneous)

Related Terms

Logarithm properties Natural log Solving exponential equations Logarithmic properties

Study This Concept

Practice solving log equations with free review games in these units:

Pre-Calculus Unit 3: Exponential and Logarithmic Functions