Question

use natural logarithms to solve the equation. $e^{4x}=18$. select the correct choice below and, if necessary, fill in the. a. $x = square$ (simplify your answer. do not round until the final a). b. the solution is not a real number.

Explanation:

Step1: Take natural log of both sides

$\ln(e^{4x})=\ln(18)$

Step2: Use log - exponent property

Since $\ln(e^{a}) = a$, we have $4x=\ln(18)$

Step3: Solve for x

$x = \frac{\ln(18)}{4}$

Answer:

A. $x=\frac{\ln(18)}{4}$