Assume that x, y and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } x ^ { 6 } y ^ { 4 }$ in terms of the logarithms of x and y.
A) $6 \log _ { c } x + 4 \log _ { c } y$
B) $24 \log _ { c } x + y$
C) $6 \log _ { c } x + 6 \log _ { c } y$
D) $24 \log _ { c } x + 4 \log _ { c } y$
E) $6 \log _ { c } x + 24 \log _ { c } y$

Question

Assume that x, y and c are positive numbers.Use the properties of logarithms to write the expression $\log _ { c } x ^ { 6 } y ^ { 4 }$ in terms of the logarithms of x and y. 
A) $6 \log _ { c } x + 4 \log _ { c } y$
B) $24 \log _ { c } x + y$
C) $6 \log _ { c } x + 6 \log _ { c } y$
D) $24 \log _ { c } x + 4 \log _ { c } y$
E) $6 \log _ { c } x + 24 \log _ { c } y$

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the power rule ($\log_b(m^n) = n \log_b(m)$) and the product rule ($\log_b(mn) = \log_b(m) + \log_b(n)$), the expression $\log_c(x^6y^4)$ can be rewritten as $6\log_c(x) + 4\log_c(y)$.

Assume That X, Y and C Are Positive Numbers log⁡cx6y4\log _ { c } x ^ { 6 } y ^ { 4 }logc​x6y4

Assume That X, Y and C Are Positive Numbers $\log _ { c } x ^ { 6 } y ^ { 4 }$