Question

How to solve this??? e^(2x) - e^x = 6

Answer 1

$e^{2x}-e^x=6$
$(e^x)^2-e^x-6=0$
$(e^x-3)(e^x+2)=0$

$e^x=3$
$e^x=-2$

therefore $x=\ln3$ and $x=\ln-2$
because $\ln-2$ doesn't exist, the only solution to your equation is $x=\ln3$