Question

If $9^{x-\frac{1}{2}}-2^{2x-2}=4^x-3^{2x-3},$ then x is

• A. $\frac{3}{2}$
• B. $\frac{2}{5}$
• C. $\frac{3}{4}$
• D. $\frac{4}{9}$

Answer 1

The correct option is A

$\frac{3}{2}$

Best way to solve this question is by simply checking for different options.
For x = 3/2
LHS = $9^{3/2–1/2}-2^{2\ast 3/2–2}=9^1-2^1=9–2=7$
RHS = $4^{3/2}–3^{2\ast 3/2–3}=8–1=7$
Since, LHS = RHS.
Therefore, x = 3/2 is our answer.