Step 1 :The given expression is a natural logarithm of a product of powers. According to the properties of logarithms, the logarithm of a product is the sum of the logarithms of the individual factors.
Step 2 :Also, the logarithm of a power is the product of the exponent and the logarithm of the base.
Step 3 :Therefore, we can rewrite the given expression as the sum of the logarithms of x, y, and z, each multiplied by their respective exponents.
Step 4 :Final Answer: \( \boxed{5 \ln x+4 \ln y+\ln z} \)