College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.6 - Logarithmic and Exponential Equations - 6.6 Assess Your Understanding: 44

Answer

$x = \dfrac{\ln{14}}{\ln{3}}\approx 2.402$

Work Step by Step

Take the natural logarithm of both sides to obtain: $\ln{3^x} = \ln{14}$ Use the rule $\ln{a^x} = x \cdot \ln{a}$ to obtain: $x\cdot \ln{3} = \ln{14}$ Divide both sides of the equation by $\ln{3}$ to obtain: $\dfrac{x\cdot \ln{3}}{\ln{3}}=\dfrac{\ln{14}}{\ln{3}} \\x = \dfrac{\ln{14}}{\ln{3}} \\x \approx 2.402$
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