6 8ln(x + 1) - 7 = 1

Explanation:

Step1: Isolate the logarithmic term

Add 7 to both sides of the equation: $8\ln(x + 1)-7+7=1 + 7$ $8\ln(x + 1)=8$

Step2: Solve for the logarithmic term

Divide both sides by 8: $\frac{8\ln(x + 1)}{8}=\frac{8}{8}$ $\ln(x + 1)=1$

Step3: Convert from logarithmic to exponential form

Recall that if $\ln a=b$, then $e^b=a$. So, since $\ln(x + 1)=1$, we have: $x + 1=e^1$ $x+1 = e$

Step4: Solve for x

Subtract 1 from both sides: $x=e - 1$

Answer:

$x=e - 1$