If 4^{x+2} = 2^{2x+3} + 2, then value of x is — WBCS Main Examination 2023 Q110

Q110

ArithmeticAlgebra, Equations & Operations

If $4^{x+2} = 2^{2x+3} + 2$, then value of $x$ is

Answer: (A) −1

$4^{x+2} = 2^{2x+4} = 2 \times 2^{2x+3}$, so the equation becomes $2^{2x+3} = 2$. Hence $2x + 3 = 1$ and $x = -1$. Check: $4^1 = 4 = 2^1 + 2$.

WBCS Main Examination 2023 — Paper VI: Arithmetic and Test of Reasoning · Question 110 of 200