Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible.
\[
5 \ln (x+8)-5 \ln x
\]
\[
5 \ln (x+8)-5 \ln x=\square
\]
Answer
\(\boxed{\ln \left(\frac{(x+8)^5}{x^5}\right)}\) is the final answer.
Step 1 ：Given the expression \(5 \ln (x+8)-5 \ln x\)
Step 2 ：We can use the properties of logarithms to condense the expression into a single logarithm. The property we will use is \(\ln a - \ln b = \ln \left(\frac{a}{b}\right)\)
Step 3 ：Applying this property to the given expression, we get \(\ln \left(\frac{(x+8)^5}{x^5}\right)\)
Step 4 ：This is the simplified form of the given expression. The coefficient of the logarithm is 1, as required. The expression cannot be evaluated further without a specific value for x.
Step 5 ：\(\boxed{\ln \left(\frac{(x+8)^5}{x^5}\right)}\) is the final answer.
