4.4 Homework

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Question 14
If $\ln (x-8)-\ln (4)=\ln (7)$, then $x=$
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Final Answer: $\boxed{36}$

Steps

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: $\boxed{36}$