Question

how to solve e^-x = (e^x)^3 * 1/e^2

Answer 1

ln of both sides
-x = ln(e^(3x)/e^2) = ln(e^(3x) - ln(e^2)
-x = 3x - 2
3x+x = 2
4x=2
x = (1/2)

Answer 2

\[e^{-x} = e{^x{^\left(3\right)}} \dot\ \frac{1}{e^2}\]
\[\frac{1}{e^x}= e{^x{^\left(3\right)}} \dot\ \frac{1}{e^2}\]
\[\frac{1}{e^x}= \frac{e{^x{^\left(3\right)}}}{e^2}\]
\[e^2= e{^x{^\left(3\right)}}*e^x\]
\[e^2= e{^x{^\left(3 + 1\right)}}\]
\[e^2= e{^x{^\left(4\right)}}\]
\[e^2= e{^{4x}}\]
\[2 = 4x\]
\[\frac{2}{4} = x\]
\[\frac{1}{2} = x\]