Chapter 12 - Section 12.3 - Exponential Functions - Exercise Set - Page 861: 25

$x=\dfrac{8}{5}$

$32^{2x-3}=2$ Rewrite $32$ as $2^{5}$: $(2^{5})^{2x-3}=2$ Multiply the exponents: $2^{10x-15}=2$ If $2^{10x-15}=2$, then $10x-15=1$: $10x-15=1$ Solve for $x$: $10x=1+15$ $10x=16$ $x=\dfrac{16}{10}$ $x=\dfrac{8}{5}$