Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-4 Properties of Logarithms - Practice and Problem-Solving Exercises - Page 466: 39



Work Step by Step

Recall the power property of logarithms (pg. 462): $\log_b{m^n}=n\log_b{m}$ We rewrite the values in the form of $m^n$, so that we can apply the power property: $\log_{2}{4}-\log_2{16}\\ =\log_{2}{2^2}-\log_2{2^4}\\ =2\log_{2}{2}-4\log_2{2}\\ =2\times1-4\times 1\\ =2-4\\ =-2$ We also used the fact that $\log_{2}{2}=1$ (because $2^1=2$).
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