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[Solved] Logarithm and inequality

 
Inequalities
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June 15, 2021 11:29 am
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Staff 
(@armor)
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Solve the inequality    lg(x^2-x-6)<lg(2-3x).

 

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June 15, 2021 11:29 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

The inequality holds if and only if 

\small x^2-x-6>0

\small 2-3x>0

\small x^2-x-6<2-3x

\small \Rightarrow

\small x<-2  or  \small x>3

\small x<\frac{2}{3}

\small -4<x<2

\small \Rightarrow -4<x<2,  which is the solution of the original inequality.

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