College Algebra (11th Edition)

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

Chapter 4 - Review Exercises: 57

Answer

$x=3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \log_2(x^3+5)=5 ,$ convert to exponential form. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to \begin{array}{l}\require{cancel} x^3+5=2^5 \\\\ x^3+5=32 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x^3=32-5 \\\\ x^3=27 \\\\ x=\sqrt[3]{27} \\\\ x=\sqrt[3]{3^3} \\\\ x=3 .\end{array}
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