Question

(2/3) ^n^2+2n= (3/2)

Answer 1

is your question -------> $\left(\frac{2}{3}\right)^{(n^2+2n)}=\left(\frac{3}{2}\right)$

we know $\frac{1}{a^x}=a^{-x}$ use it here to solve the question.

so, $\left(\frac{2}{3}\right)^{(n^2+2n)}=\left(\frac{2}{3}\right)^{-1}$

now use concept , $a^x=a^y\implies x=y$

so, n² + 2n = -1

n² + 2n + 1 = 0

(n + 1)² = 0

n = -1

hence value of n = -1