Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Concept Check - Page 388: 5

Answer

a. $\log_{a}x=y \Leftrightarrow a^{y}=x$, see step-by-step b. logarithm with base $e$ c. logarithm with base 10 d. $7^{2}=49$

Work Step by Step

a. The logarithmic function $\log_{a}$ with base $a ($where $a>0, a\neq 1)$ is defined for $x > 0$ by $\log_{a}x=y \Leftrightarrow a^{y}=x$ ( $\log_{a}x$ is the exponent to which the base $a$ must be raised to give $x$) b. The natural logarithm is the logarithm with base $e.$ c. The common logarithm is the logarithm with base 10. d. $\log_{a}x=y \Leftrightarrow a^{y}=x$ $\log_{7}49=2$ , the logarithmic form, is equivalent to $7^{2}=49$, the exponential form.
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