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

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 $\log_b(yz^5)$ gives $\log_b(y) + 5\log_b(z)$.

Rewrite Using the Pow Er and Product Rules log⁡byz5\log _{\mathrm{b}} \mathrm{yz}^{5}logb​yz5

Rewrite Using the Pow Er and Product Rules $\log _{\mathrm{b}} \mathrm{yz}^{5}$