College Algebra (11th Edition)

$x=\dfrac{e^{1.5}}{4}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\ln(4x)=1.5 ,$ convert it to exponential form. $\bf{\text{Solution Details:}}$ Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e(4x)=1.5 .\end{array} Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is \begin{array}{l}\require{cancel} e^{1.5}=4x \\\\ 4x=e^{1.5} \\\\ x=\dfrac{e^{1.5}}{4} .\end{array}