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Lesson eLearning

Solve for $x$ in the equation $2^{x} \times 4^{, x - 1} = 8^{3}$ .

hard 3 marks Class 7 · Mathematics · Exponents and Powers

Answer

11/3

The correct answer is 11/3 — Step 6: Solve for $x$ : $3 x = 11; R i g h t a r r o w; x = 11/3$ .

Step-by-step solution

Step 1: Express all bases as powers of 2: $4 = 2^{2}$ , $8 = 2^{3}$ .
Step 2: Rewrite the equation: $2^{x} \times (2^{2})^{x - 1} = (2^{3})^{3}$ .
Step 3: Simplify the powers: $2^{x} \times 2^{2 x - 2} = 2^{9}$ .
Step 4: Combine exponents on the left: $2^{x + 2 x - 2} = 2^{3 x - 2}$ .
Step 5: Since bases are equal, equate exponents: $3 x - 2 = 9$ .
Step 6: Solve for $x$ : $3 x = 11; R i g h t a r r o w; x = 11/3$ .

Common mistake: Not rewriting all terms with the same base before equating exponents.

Concept tested: Solving exponential equations

Published 16 October 2026 · How this solution was prepared and checked

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