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

Expert Answers
justaguide eNotes educator| Certified Educator

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

always-curious | Student

I agree with your answer, this was what I worked out too. But here we are assuming that the base is greater than zero so how will we check when base is greater than zero but smaller than one ?

Also, won't we have to exclude the point -4/3 where base becomes equal to 1?

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