Verified Answer :

You can essentially treat this equation as a factorable quadratic, with the variable being \(e^x\):

\(e^{2x} - 3e^x + 2 = 0\)
\((e^x - 2)(e^x - 1) = 0\)
\(e^x = 1, 2\)
\(x = \ln 1, \ln 2 = 0, \ln 2\)