Grade 11 · Theory
Exponential equations
Exponents and surds · about 3 min
Visual overview: Exponential equations1 MIN READ
2 study sections · pause after each one and recall the key ideaExponential equations hide the unknown in the exponent; the trick is to make the bases match.
Key points- 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.
EXAM TIP
4ˣ = 8 becomes 2²ˣ = 2³, so 2x = 3 — prime bases unlock almost every question.