What is the solution of : log(3x+5) (9x*x + 8*x +2) > 2?

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We have to solve: log(3x + 5) (9x*x + 8*x +2) > 2

log(3x + 5) (9x*x + 8*x +2) > 2

=> 9x*x + 8*x +2 > (3x + 5)^2

=> 9x^2 + 8x + 2 > 9x^2 + 30x + 25

=> 8x - 30x > 25 -...

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We have to solve: log(3x + 5) (9x*x + 8*x +2) > 2

log(3x + 5) (9x*x + 8*x +2) > 2

=> 9x*x + 8*x +2 > (3x + 5)^2

=> 9x^2 + 8x + 2 > 9x^2 + 30x + 25

=> 8x - 30x > 25 - 2

=> -22x > 23

=> x < -23/22

But the base of the logarithm has to be greater than 0

=> 3x + 5 > 0

=> x > -5/3

The solution of the inequality is -5/3 < x < -23/22

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