Exponential and log equations

Same base, drop it

If you can write both sides with the same base, the exponents must be equal. 2ˣ = 8 becomes 2ˣ = 2³, so x = 3.

Otherwise take logs

Take ln of both sides and bring the exponent down: ln(aˣ) = x·ln(a). That is what log rules are for.

Check every answer

Log equations produce extraneous solutions constantly. Any answer that makes the inside of a log zero or negative is not a solution, however good the algebra was.