Question

2 log(5x-1)-log(3x+2)^2=2

Answer 1

$2 log(5x - 1) - log(3x + 2) {}^{2} = 2 \\ 2 log(5x - 1) - log((3x + 2) {}^{2} ) = 2 \\ log((5x - 1) {}^{2} ) - log((3x + 2) {}^{2} ) = 2 \\ log( \frac{5x - 1 {}^{2} }{3x + 2 {}^{2} } ) = 2 \\ {5x - 1 {}^{2} }{3x + 2 {}^{2} } = 100 \\ \frac{5x - 1}{3x + 2} = \binom{ + }{ - } 10 \\ \frac{5x - 1}{3x + 2 } = + 10 \\ \frac{5x - 1}{3x + 2} = - 10 \\ x = - \frac {21} {25} \\ orx = - \frac{19}{35}$

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