## Precalculus: Mathematics for Calculus, 7th Edition

$\log_{2}(\dfrac{s^{5}}{7t^2})=5\log_{2}s-\log_{2}7-2\log_{2}t$
$\log_{2}(\dfrac{s^{5}}{7t^2})$ We begin the expanding process, noting that a division can be expanded as a substraction: $\log_{2}(\dfrac{s^{5}}{7t^2})=\log_{2}(s^{5})-\log_{2}(7t^{2})$ We expand the product in $\log_{2}(7t^{2})$ as a sum: $...=\log_{2}(s^{5})-[\log_{2}(7)+\log_{2}(t^{2})]=...$ $...=\log_{2}(s^{5})-\log_{2}(7)-\log_{2}(t^{2})=...$ The exponents in $\log_{2}(s^{5})$ and $\log_{2}(t^{2})$ can be taken to the front of the logarithm to multiply: $...=5\log_{2}s-\log_{2}7-2\log_{2}t$