Question 1:

Expression: $\ln(x(x+4)(x+8))$

Using the laws of logarithms:

1. Expand the natural log: $\ln(x(x+4)(x+8)) = \ln(x) + \ln(x+4) + \ln(x+8)$

This is the simplified expanded form.

Question 2:

Equation: $\log_3(x) = 2$

Using the definition of logarithms: $x = 3^2 = 9$

Thus, $x = 9$.

Would you like a detailed step-by-step breakdown of either solution? Here are 5 related questions to expand your understanding:

1. How can you use the logarithmic laws to condense an expression?
2. What are the steps to solve logarithmic equations like $\log_b(x) = y$?
3. How do logarithms relate to exponential functions?
4. How can you apply the change of base formula for logarithms?
5. What are the common properties of natural logarithms?

Tip: Always verify the domain of logarithmic functions to ensure arguments are positive!