Solveeit Logo
Login

Question

Question: If \(\left( \frac{2}{3} \right)^{x + 2} = \left( \frac{3}{2} \right)^{2 - 2x},\) then x =...

If (23)x+2=(32)2−2x,\left( \frac{2}{3} \right)^{x + 2} = \left( \frac{3}{2} \right)^{2 - 2x}, then x =

A

1

B

3

C

4

D

0

Answer

4

Explanation

Solution

(23)x+2=(32)2−2x\left( \frac{2}{3} \right)^{x + 2} = \left( \frac{3}{2} \right)^{2 - 2x} ⇒ (23)x+2=(22)2−2x\left( \frac{2}{3} \right)^{x + 2} = \left( \frac{2}{2} \right)^{2 - 2x}.

Clearly x+2=2x−2x + 2 = 2x - 2 ⇒ x=4x = 4