Exponential equation

An equation with the variable in the exponent, e.g. 3ˣ⁺¹ = 27. CAPS Grade 10 definition, worked example and related algebra practice.

An equation with the variable in the exponent, e.g. 3ˣ⁺¹ = 27.

Definition

An exponential equation has the unknown in an exponent. In Grades 10 and 11 you solve it by writing both sides with the same base and then setting the exponents equal. Grade 12 adds logarithms for bases that can't be matched.

Worked example

3ˣ⁺¹ = 27 = 3³, so x + 1 = 3 and x = 2.

2ˣ⁺¹ + 2ˣ = 12: factorise to 2ˣ(2 + 1) = 12, so 2ˣ = 4 and x = 2.

Where it appears in the exam

Exponential equation is part of the algebra section of CAPS Grade 10 Mathematics and is examined in Paper 1 of the November exam.

Step-by-step method

  1. Write each number as a power of a prime base.
  2. If terms are added, factorise out the common power first.
  3. Make the bases on both sides equal.
  4. Set the exponents equal and solve.

Common mistake

Applying the exponent laws to a sum, e.g. treating 2ˣ⁺¹ + 2ˣ as 2²ˣ⁺¹.

Related algebra terms

Frequently asked questions

What does exponential equation mean in Grade 10 Maths?

An exponential equation has the unknown in an exponent. In Grades 10 and 11 you solve it by writing both sides with the same base and then setting the exponents equal. Grade 12 adds logarithms for bases that can't be matched.

Which paper tests exponential equation in Grade 10?

Exponential equation belongs to the Algebra section of CAPS Grade 10 Mathematics, which is examined in Paper 1 of the November exam.

How do I practise questions involving exponential equation?

Snap a question that uses exponential equation into Snap&Learn with your grade set to Grade 10, or work through the Grade 10 topic guide and practice papers.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.