Inverse of a function $e^x + 2e^{2x}$ The function is $f(x) = e^x+2e^{2x}$
So to find the inverse I went
$$WTS: x = ____$$
$$y =  e^x+2e^{2x}$$
$$ log3(y)=log3(3e^{2x})$$
$$ log3(y) = 2x$$
$$ log3(y)=5x$$
$$ x=\frac{log3(y)}{2}$$
Am i correct?

No, you are wrong, $log$ is not a linear function,  set $g(x)=e^x$, $2g(x)^2+g(x)-y=0$，
solving this equation, since $y>0$, $g(x)=e^x=-{1\over4}+{1\over 2}\sqrt{{1\over4}+2y}.$
