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Solve log(3x -2) x^(2) gt log (3x-2) (...

Solve ` log_(3x -2) x^(2) gt log _(3x-2) (3x -2)`

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To solve the inequality \( \log_{(3x - 2)}(x^2) > \log_{(3x - 2)}(3x - 2) \), we will analyze the conditions under which this inequality holds true. ### Step 1: Identify the base of the logarithm The base of the logarithm, \( 3x - 2 \), must be positive and not equal to 1: 1. \( 3x - 2 > 0 \) implies \( x > \frac{2}{3} \) 2. \( 3x - 2 \neq 1 \) implies \( 3x \neq 3 \) or \( x \neq 1 \) ### Step 2: Rewrite the inequality ...
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