College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check - Page 425: 62


$x\approx 3.07$

Work Step by Step

Take the natural log of both sides to obtain: $\ln{(e^{\frac{3x}{4}})} = \ln{10}$ Use the rule $\log{(a^n)} = n\cdot\log{a}$ to obtain: $\frac{3x}{4} \cdot \ln{e} = \ln{10}$ Use the rule $\ln{e} = 1$ to obtain: $\frac{3x}{4} \cdot 1 = \ln{10} \\\frac{3x}{4}= \ln{10}$ Multiply $\frac{4}{3}$ to both sides of the equation to obtain: $\frac{3x}{4} \cdot \frac{4}{3}= \frac{4}{3} \cdot \ln{10} \\x= \frac{4\ln{10}}{3}$ Use a calculator to obtain: $x\approx 3.07$
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