Solving exponential equations

Math

Definition

Finding the value of the variable in equations where the unknown appears in an exponent. Common techniques include rewriting both sides with the same base, or taking the logarithm of both sides.

How It Works

  1. Isolate the exponential expression on one side if possible.
  2. If both sides can be written with the same base, set the exponents equal.
  3. Otherwise, take the logarithm of both sides.
  4. Use logarithm properties to bring the exponent down.
  5. Solve for the variable.

Examples

  • 2ˣ = 16 → 2ˣ = 2⁴ → x = 4
  • 5ˣ = 30 → x = ln(30)/ln(5) ≈ 2.11

Related Terms

Logarithm properties Natural log Exponent rules Exponential growth and decay

Study This Concept

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

Algebra 2 Unit 7: Exponential and Logarithmic Functions