Assume that x, y, and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y.
A) $\log _ { c } 5 + \log _ { c } x y$
B) $\log _ { c } 5 + \log _ { c } x + \log _ { c } y$
C) $\log _ { c } 5 + \log _ { c } x$
D) $\log _ { c } 5 + \log _ { 5 } x + \log _ { 5 } y$
E) $\log _ { c } 5 + \log _ { c } y$

Question

Assume that x, y, and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } 5 x y$ in terms of the logarithms of x and y. 
A) $\log _ { c } 5 + \log _ { c } x y$
B) $\log _ { c } 5 + \log _ { c } x + \log _ { c } y$
C) $\log _ { c } 5 + \log _ { c } x$
D) $\log _ { c } 5 + \log _ { 5 } x + \log _ { 5 } y$
E) $\log _ { c } 5 + \log _ { c } y$

Quizplus · Accepted Answer

The properties of logarithms state that $\log_b(mn) = \log_b(m) + \log_b(n)$ and can be applied here to split $\log_c(5xy)$ into $\log_c(5) + \log_c(x) + \log_c(y)$.

Assume That X, Y, and C Are Positive Numbers log⁡c5xy\log _ { c } 5 x ylogc​5xy

Assume That X, Y, and C Are Positive Numbers $\log _ { c } 5 x y$