Question

If 8^x = 32/2^x, find x.
1. 8/7
2. 2/9
3. 5/4
4. 3/4

Answer 1

Correct Answer - Option 3 : 5/4

Given:

8^x = 32/2^x

Formula used:

pⁿp^m = p^m+n

(pⁿ)^m = p^mn

pⁿqⁿ = (pq)ⁿ

p^m ÷ pⁿ = p^m-n

Calculation:

8^x = 32/2^x

⇒ (2³)^x = 2⁵/2^x

⇒ 2^3x = 2^5-x

On comparing powers

⇒ 3x = 5 – x

⇒ 4x = 5

⇒ x = 5/4

∴ The value of x is 5/4.