Question

If \(2^{2x-1}+4^x=3^{x-\frac{1}{2}}+3^{x+\frac{1}{2}}\), then x equals

• A. 1/2
• B. 2/3
• C. 1
• D. 3/2

Answer 1

The Correct Option is D

\(\text{Expression: } 2^{2x-1} + 4^x = 3^{x-\frac{1}{2}} + 3^{x+2}\)
\(\Rightarrow 2^{2x} + 2^{2x} = 3^{x} \sqrt{3} + \left( 3^x \times \sqrt{3} \right)\)
\(\Rightarrow 2^{2x} \left( 2 + 1 \right) = 3^x \left( \sqrt{3} + \sqrt{3} \right)\)
\(\Rightarrow 2^{2x} \times \frac{3}{2} = 3^x \times \frac{4}{\sqrt{3}}\)
\(\Rightarrow 2^{2x-1} \times 3^1 = 3^{x-2} \times 2^2\)
\(\text{Now, comparing powers of (any one of) 2 or 3, we get: } x = \frac{3}{2}\)

The correct answer is (D) :3/2