Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 295: 59



Work Step by Step

We know that if the graph of $f(x)=\log_a{x}$ contains the point $(2,2)$, then $2=\log_a{2}$. We know that if $y=\log_a{b}$, then $a^y=b$. Hence here: $a^2=2\\a=\pm\sqrt2.$ But the base of a logarithm can only be positive, hence $a=\sqrt2.$
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