## Precalculus (6th Edition) Blitzer

$\log(x^6y^2)$
Recall the log rules: (a) $\log_b{p \cdot q} =\log p + \log q$ (b) $\log_b{\dfrac{p}{q}}=\log_b{p} - \log_b{q}$ (Quotient Rule). (c) $\log{a^n}=n \log x$ (d) $\log_a{a^x}=x$ Use the rule (a) with $p=x^6$ and $q=y^2$ to obtain $6 \log x+2 \log y=\log x^6 +\log y^2$ Simplify the second term by applying rule (c) to obtain: $\log x^6 +\log y^2= \log(x^6y^2)$