Algebra 2 Common Core

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

Chapter 7 - Exponential and Logarithmic Functions - 7-3 Logarithmic Functions as Inverses - Practice and Problem-Solving Exercises - Page 458: 81



Work Step by Step

Recall (1) $\log_a{b}=y \longleftrightarrow a^y=b$ (2) The value of the function $f(x)=\log_a{x}$ increases as $x$ increases. Let $y=\log_{1.5}{2.5}$ Use the definition in (1) above to obtain: $1.5^y=2.5$ Note that $1.5^2=2.25$ while $1.5^3=3.375$ Since $2.25\lt 2.5 \lt 3.375$, then $y$ must be between $2$ and $3$. Thus, the least integer that is greater than $\log_{1.5}{2.5}$ is $3$.
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