Exercise 63 Page 970

To write the given logarithmic expression as a single logarithm, we will first recall the Product Property, Quotient Property, and Power Property of Logarithms. Product:& log_b mn = log_b m + log_b n Quotient:& log_b mn = log_b m - log_b n Power:& log_b a^m = m log_b a In the above formulas, m, n, and b are positive numbers, where b≠ 1. Let's apply these properties to simplify our expression.

4log_3 x + log_3 y -2log_3 z

m* log_3(a)=log_3(a^m)

log_3 x^4 + log_3 y -log_3 z^2

log_3(m) + log_3(n)=log_3(mn)

log_3 (x^4 y)-log_3 z^2

log_3(m) - log_3(n)=log_3(m/n)

log_3x^4y/z^2

This corresponds to option A.