Question

Resolver: e^2x-8e^x=0

Answer 1

$e^{2x}-8e^x=0 \\ \\ (e^x)^2-8e^x=0 \\ \\ Substitua: \ y=e^x \\ \\ y^2-8y=0 \\ \\ y(y-8)=0 \\ \\ y=0 \\ \\ y=2\sqrt2 \\ \\ retornando \ variavel \ x: \\ \\ e^x=0 \rightarrow \ \ \ sem \ solucao \\ \\ \boxed{e^x=2\sqrt2 \rightarrow x=\frac{3ln2}{2}}$