Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x\approx1.134$
Using the properties of equality, the given equation, $29=3e^{2x} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{29}{3}=e^{2x} .\end{array} Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $\dfrac{29}{3}=e^{2x} ,$ is \begin{array}{l}\require{cancel} \ln\dfrac{29}{3}=\ln e^{2x} \\\\ \ln\dfrac{29}{3}=2x(\ln e) \\\\ \ln\dfrac{29}{3}=2x(1) \\\\ \ln\dfrac{29}{3}=2x \\\\ \dfrac{\ln\dfrac{29}{3}}{2}=x \\\\ x\approx1.134 .\end{array}