Question

how do you reduce ln(3^-e e^3) to simplest form

Answer 1

The logarithm of a product is equal to the sum of logarithms:

$\ln(3^{-e}e^3)=\ln3^{-e}+\ln e^3$

Drop the exponents:

$-e\ln3+3\ln e$

The logarithm of a number is equal to 1 if the base of the logarithm is the same as the number itself:

$-e\ln3+3$