Question

Why does 1+12e^(-x)=e^(x) simplify to x=ln(4)?? Thanks

Answer 1

try multiplying both sides by e^x \[e^x(1+12e^{-x})=e^x e^x \\ e^x+12=e^{2x} \\e^{2x}-e^x-12=0\]

Answer 2

this is a quadratic in terms of e^x

Answer 3

Ah, I see, thanks!