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: 34


$\dfrac{\log_{10}{7}}{\log_{10}{4}}\approx 1.40$

Work Step by Step

Recall the change of base formula (pg. 464): $\log_{b}{m}=\dfrac{\log_{c}{m}}{\log_{c}{b}}$ Since most calculators use base $10$ logarithms ($\log{x}=\log_{10}{x}$), we can evaluate the expression by rewriting it in base $10$ and using a calculator: $\log_{4}{7}=\dfrac{\log_{10}{7}}{\log_{10}{4}}\approx 1.40$
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