## College Algebra (10th Edition)

Published by Pearson

# Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding - Page 450: 92

#### Answer

$x=\dfrac{11}{3}$

#### Work Step by Step

RECALL: $\log_a{x} = y \longrightarrow a^y=x$ Use the definition above to obtain: $\log_3{(3x-2)}=2 \\ \longrightarrow 3^2=3x-2 \\9=3x-2$ Add 2 on both sides of the equation to obtain: $\begin{array}{ccc} &9+2&= &3x-2+2 \\&11 &= &3x\end{array}$ Divide 3 on both sides of the equation to obtain: $\frac{11}{3}=\frac{3x}{3} \\\frac{11}{3}=x$

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