Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions - Concept and Vocabulary Check - Page 474: 8

Answer

The function \[y={{\log }_{b}}x\] is equivalent to the exponential form \[{{b}^{y}}=x\ \]and\[x>0,b>0,b\ne 1\].

Work Step by Step

The provided function is \[y={{\log }_{b}}x\]with base b also, logarithmic and exponential functions are inverse functions of each other,therefore, taking anti log on both sides of the provided function the resulted function is\[{{b}^{y}}=x\ \]. The resulted function is the exponential form of the provided function with base b and exponent\[y\].
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