## Algebra 2 Common Core

$\log{4} + 4\log{s}+\log{t}$
RECALL: (1) Product Property of Logarithms: $\log_a{mn}=\log_a{m} + \log_a{n}$ (2) Quotient Property of Logarithms: $\log_a{\frac{m}{n}}=\log_a{m} - \log_a{n}$ (3) Power Property of Logarithms: $\log_a{m^n}=n\log_a{m}$ Use the Product Property to obtain: \begin{align*} \log{4s^4t}&=\log{4s^4}+\log{t}\\ &=\log{4} + \log{s^4}+\log{t} \end{align*} Use the Power Property to obtain: $$\log{4} + \log{s^4}+\log{t}=\log{4} + 4\log{s}+\log{t}$$