Solving Equations with Logs

Type 1: log_ax = b

Convert to index form: x = a^b

Example: log₂x = 5   ⇒   x = 2⁵ = 32

Type 2: Same base both sides

If log_ax = log_ay then x = y

Example: log x + log 2 = log 14   ⇒   log(2x) = log 14   ⇒   2x = 14   ⇒   x = 7

Check: The argument of every log must be positive in the final answer.

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