## College Algebra (11th Edition)

$x=6$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\ln e^x-\ln e^3=\ln e^3 ,$ use the properties of logarithms to simplify the logarithmic expressions. Then do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent \begin{array}{l}\require{cancel} x\ln e-3\ln e=3\ln e .\end{array} Since $\ln e=1,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x(1)-3(1)=3(1) \\\\ x-3=3 \\\\ x=3+3 \\\\ x=6 .\end{array} Upon checking, $x=6$ satisfies the original equation.