Question

question
solve for the exact value of $x$.
$4\ln(4x - 3) + 8 = 16$
answer attempt 1 out of 5

Explanation:

Step1: Isolate the logarithmic term

Subtract 8 from both sides.
$4\ln(4x - 3) = 16 - 8$
$4\ln(4x - 3) = 8$

Step2: Simplify the coefficient

Divide both sides by 4.
$\ln(4x - 3) = \frac{8}{4}$
$\ln(4x - 3) = 2$

Step3: Convert to exponential form

Use $e^{\ln(a)} = a$ to eliminate the natural log.
$4x - 3 = e^2$

Step4: Isolate x

Add 3 to both sides, then divide by 4.
$4x = e^2 + 3$
$x = \frac{e^2 + 3}{4}$

Answer:

$x = \frac{e^2 + 3}{4}$