Smart Math guide · Advanced Math Ideas

Translate Logarithms into Exponents

A logarithm answers: what exponent on the base produces this number?

All levelsWorked example includedSelf-check included
The method

How to use it

  1. Rewrite log_b(a)=c as b^c=a.
  2. Use product, quotient, and power laws only where their conditions hold.
  3. Check domain: log arguments must be positive in real-number work.
Worked example

See it in action

log₂32=5 because 2⁵=32.

Check your thinking

How to verify it

Evaluate the exponential form to verify.