4.4 Homework Score: 0/100 0/14 answered Question 14 If $\ln (x-8)-\ln (4)=\ln (7)$, then $x=$ Submit Question

Step 1 ：Apply the logarithmic property \(\ln a - \ln b = \ln \frac{a}{b}\) to the left side of the equation to get \(\ln \frac{x-8}{4} = \ln 7\).

Step 2 ：Since the logarithms on both sides of the equation are equal, their arguments must also be equal. Therefore, \(\frac{x-8}{4} = 7\).

Step 3 ：Solve the equation \(\frac{x-8}{4} = 7\) for x to get \(x = 36\).

Step 4 ：The solution to the equation is \(x = 36\). This means that when \(x = 36\), the original logarithmic equation holds true.

Step 5 ：Final Answer: \(\boxed{36}\)