14. -6e^8x + 8 - 3 = -23 +3 +3 -6e^8x + 8 = -20 / -6 / -6

Explanation:

Step1: Isolate the exponential - term

Add 3 to both sides of the equation $-6e^{8x + 8}-3=-23$. $-6e^{8x + 8}-3 + 3=-23 + 3$ $-6e^{8x + 8}=-20$

Step2: Solve for the exponential - term

Divide both sides by - 6. $\frac{-6e^{8x + 8}}{-6}=\frac{-20}{-6}$ $e^{8x + 8}=\frac{10}{3}$

Step3: Take the natural logarithm of both sides

$\ln(e^{8x + 8})=\ln(\frac{10}{3})$ Since $\ln(e^{a}) = a$, we have $8x+8=\ln(\frac{10}{3})$

Step4: Solve for x

First, subtract 8 from both sides: $8x=\ln(\frac{10}{3})-8$ Then divide both sides by 8: $x=\frac{\ln(\frac{10}{3})-8}{8}$

Answer:

$x=\frac{\ln(\frac{10}{3})-8}{8}$