Exponential equations

Exponential equations hide the unknown in the exponent; the trick is to make the bases match.

• Write both sides with the SAME base, then equate the exponents.
• Factorise when several exponential terms appear, treating aˣ as a single variable.
• Some equations reduce to a quadratic in aˣ — substitute k = aˣ.
• Check for invalid solutions: aˣ can never be negative or zero.

• Exponential equation — an equation with the variable in the exponent.