Rewrite using the pow er and product rules. Assume all variables represent positive real numbers.
-$\log _{a} 5 x^{4} y z^{6}$
A) $\log _{a} 5+4 \log _{a} x+\log _{a} y+6 \log _{a} z$
B) $24 \log _{a} 5 x y z$
C) $5+\log _{\mathrm{a}} y+\log _{\mathrm{a}} \mathrm{z} 6$
D) $\log _{a} 5-4 \log _{a} x-\log _{a} y-6 \log _{a} z$

Question

Quizplus · Accepted Answer

The product rule of logarithms states that $\log_b(mn) = \log_b(m) + \log_b(n)$, and the power rule states that $\log_b(m^n) = n\log_b(m)$. Applying these rules to $\log_a(5x^4yz^6)$ results in $\log_a(5) + 4\log_a(x) + \log_a(y) + 6\log_a(z)$.

Rewrite Using the Pow Er and Product Rules log⁡a5x4yz6\log _{a} 5 x^{4} y z^{6}loga​5x4yz6

Rewrite Using the Pow Er and Product Rules $\log _{a} 5 x^{4} y z^{6}$