College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.3 - Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions: 27

Answer

$x=2$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 3x=7^{\log_7 6} ,$ use the properties of logarithms to find an equivalent expression for the logarithmic expression. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using a property of logarithms which is given by $b^{\log_b x}=x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 3x=6 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x=\dfrac{6}{3} \\\\ x=2 .\end{array}
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