College Algebra (11th Edition)

$x=\dfrac{e^{16}}{5}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\ln(5x)=16 ,$ use the definition of natural logarithms and convert to exponential form. Finally, use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e(5x)=16 .\end{array} Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to \begin{array}{l}\require{cancel} 5x=e^{16} .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x=\dfrac{e^{16}}{5} .\end{array}