Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 42

$x=1.099$ $x=0.693$

$e^{2x}-5e^x+6=0$ $(e^x)^2-5e^x+6=0~~$ ($a=1,b=-5,c=6$): $e^x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-(-5)±\sqrt {(-5)^2-4(1)(6)}}{2(1)}=\frac{5±\sqrt {1}}{2}=\frac{5±1}{2}$ $e^x=3$ $\ln e^x=\ln3$ $x=1.099$ $e^x=2$ $\ln e^x=\ln2$ $x=0.693$