College Algebra (11th Edition)

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

Chapter 4 - Test: 12

Answer

$x\approx0.631$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 9^x=4 ,$ take the logarithm of both sides. Use the properties of logarithms and of equality to isolate the variable. Approximate the answer with $3$ decimal places. $\bf{\text{Solution Details:}}$ Taking the logarithm of both sides results to \begin{array}{l}\require{cancel} \log9^x=\log4 .\end{array} Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent \begin{array}{l}\require{cancel} x\log9=\log4 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x=\dfrac{\log4}{\log9} \\\\ x\approx0.631 .\end{array}
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