Answer
$x=\dfrac{\ln\dfrac{17}{2}}{12}\approx0.178339$
Work Step by Step
$2e^{12x}=17$
Take the $2$ to divide the right side of the equation:
$e^{12x}=\dfrac{17}{2}$
Apply $\ln$ to both sides:
$\ln e^{12x}=\ln\dfrac{17}{2}$
Take down the exponent $12x$ to multiply in front of the $\ln$:
$12x\ln e=\ln\dfrac{17}{2}$
Since $\ln e=1$, the equation becomes:
$12x=\ln\dfrac{17}{2}$
Solve for $x$:
$x=\dfrac{\ln\dfrac{17}{2}}{12}\approx0.178339$