Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 8



Work Step by Step

The domain of the variable requires that $3x-1>0$. Thus, $3x>1\\ x>\dfrac{1}{3}$ Recall: $y = \log_a b \text{ is equivalent to } b=a^y$. Therefore, $\log_3 (3x-1) = 2 \text{ is equivalent to } 3x-1 = 3^2$ Solve the equation to obtain: $3x-1 = 3^2$ $3x-1 = 9$ $3x = 9+1$ $3x=10$ $x=\boxed{\frac{10}{3}}$
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