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Year 10 · Functions & Graphs

Exponential and logarithmic equations

To solve an exponential equation, write both sides as powers of the same base, then equate the indices. Logs undo exponentials.

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How to do it

  1. Rewrite the number as a power of the base.
  2. Set the indices equal.
  3. log_b x = n means x = bⁿ.

Worked example

Solve for x: 3^(x + 3) = 27
3^(x + 3) = 3³, so x + 3 = 3 and x = 0.
Answer: 0

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Match the bases before comparing powers.

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