question solve for the exact value of x. 6 ln(8x - 3) - 4 = -22

Explanation:

Step1: Isolate the logarithmic term

Add 4 to both sides of the equation: $6\ln(8x - 3)-4 + 4=-22 + 4$ $6\ln(8x - 3)=-18$

Step2: Solve for the natural - logarithm term

Divide both sides by 6: $\frac{6\ln(8x - 3)}{6}=\frac{-18}{6}$ $\ln(8x - 3)=-3$

Step3: Convert the logarithmic equation to an exponential equation

Recall that if $\ln a = b$, then $a = e^{b}$. So, $8x-3=e^{-3}$

Step4: Solve for x

Add 3 to both sides: $8x=e^{-3}+3$ Divide both sides by 8: $x=\frac{e^{-3}+3}{8}$

Answer:

$x=\frac{e^{-3}+3}{8}$