Question

what is the true solution to $2\ln e^{\ln 5x} = 2\ln 15$?\
$x = 3$\
$x = 15$\
$x = 9$\
$x = 0$

Explanation:

Step1: Simplify both sides by 2

$\frac{2\ln e^{\ln 5x}}{2} = \frac{2\ln 15}{2}$
$\ln e^{\ln 5x} = \ln 15$

Step2: Apply $\ln e^a = a$ rule

$\ln 5x = \ln 15$

Step3: Cancel natural logs

$5x = 15$

Step4: Solve for x

$x = \frac{15}{5} = 3$

Answer:

$x = 3$