Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.5 - Logarithmic Functions - Exercise Set: 94c

Answer

$f(.027)=3$

Work Step by Step

We are given that $f(x)=log_{.3}x$ and that $g(x)=.3^{x}$ is the inverse of $f(x)$. We are also told that the ordered pair (3,.027) is a solution of the function $g(x)$. As seen in Section 9.2, when the ordered pair $(x_{1},y_{1})$ is a solution to a function, that function's inverse will have a solution of $(y_{1},x_{1})$. Therefore, the ordered pair $(.027,3)$ will be a solution of $f(x)$. This is written in function notation as $f(.027)=3$, which tells us that $f(x)$ has a value of 3 when $x=.027$. $f(.027)=log_{.3}.027=3$
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