Question

say the crt answer.i will mark u as brainliest​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The given expression is }\dfrac{2^{2x-1}}{2^{x+2}} = 4$

       $\text{We can write 4 as }2^{2}$

$\implies \dfrac{2^{2x-1}}{2^{x+2}} = 2^{2}$

        $\text{We know that }\dfrac{a^{m}}{a^{n}} = a^{m-n}$

$\implies 2^{2x-1-(x+2)} = 2^{2}$

       $\text{Simplifying...}$

$\implies 2^{2x-1-x-2} = 2^{2}$

       $\text{Simplifying...}$

$\implies 2^{x-3} = 2^{2}$

       $\text{Comparing the two exponents}$

$\implies x-3 = 2$

       $\text{Transposing 3 to R.H.S}$

$\implies x = 3 + 2$

       $\text{Simplifying...}$

$\implies \boxed{x = 5}$