## Precalculus: Mathematics for Calculus, 7th Edition

$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$ $\log_2 16^{23}$ Use the Third Law of Logarithms: $\log x^a = a\log x$ $$\log_2 16^{23} = 23\log_2 16$$ Rewrite 16 as $2^4$ $$23\log_2 2^4$$ Use the Third Property of Logarithms: $\log_a a^x = x$ $$23\log_2 2^4 = 23\times4 = 92$$