Answer:

Explanation:
Given logarithmic expression:
![7\left[\ln(z)+\ln(z+8)\right]-7\ln(z-8)](https://img.qammunity.org/2024/formulas/mathematics/college/nrjxc4l4pjz4m6qedmouad2vh0vzl1xnr4.png)
To simplify the expression, we can use the rules of logarithms.

Apply the product rule to the first parentheses:
![7\left[\ln(z(z+8))\right]-7\ln(z-8)](https://img.qammunity.org/2024/formulas/mathematics/college/l4ybade8mfummbljx30e7f4fb07j44kw0l.png)
Simplify:


Apply the power rule:

Apply the quotient rule:

Using the power of a quotient exponent rule, this can be be written as:
