Answer
See graph and explanations.
Work Step by Step
a. We can graph both $f(x)=ln(3x)$ and $g(x)=ln3+ln(x)$ (red) as shown in the figure; it appears that they are identical.
b. We can graph both $f(x)=ln(5x^2)$ and $g(x)=ln5+ln(x^2)$ (blue) as shown in the figure; it appears that they are identical.
c. We can graph both $f(x)=ln(2x^3)$ and $g(x)=ln2+ln(x^3)$ (green) as shown in the figure; it appears that they are identical.
d. We can observe from parts (a)-(c) that the two corresponding functions are identical or equivalent, which means that $log_b(MN)=log_b(M)+log_b(N)$
e. We can complete the statement as: The logarithm of a product is equal to the sum of the logarithms of each factor.
