College Algebra (11th Edition)

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

Chapter 4 - Review Exercises - Page 469: 36



Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 4^x=12 ,$ take the logarithm of both sides. Then use the laws of logarithms to isolate the variable. Express the answer with $3$ decimal places. $\bf{\text{Solution Details:}}$ Taking the logarithm of both sides, the equation above is equivalent to \begin{array}{l}\require{cancel} \log4^x=\log12 .\end{array} Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the equation above is equivalent to \begin{array}{l}\require{cancel} x\log4=\log12 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} \dfrac{x\log4}{\log4}=\dfrac{\log12}{\log4} \\\\ x=\dfrac{\log12}{\log4} \\\\ x\approx1.792 .\end{array}
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