Logarithmic Inequalities

**PranavArora** · May 25th 2011, 08:27 PM

I am doing a lot of questions on logarithmic inequality but i am stuck at one question:-

I dont from where to start.
Please help.

**FernandoRevilla** · May 25th 2011, 08:36 PM

Use that the inequality $\log_3 y\geq 0$ is equivalent to $y\geq 1$

**PranavArora** · May 25th 2011, 09:33 PM

Originally Posted by FernandoRevilla

Use that the inequality $\log_3 y\geq 0$ is equivalent to $y\geq 1$

Thanks for your reply but i want to know how to get rid of modulus...

**FernandoRevilla** · May 25th 2011, 11:08 PM

We have $x^2+|x-5|>0$ for all $x\in\mathbb{R}$ so, the inequality is equivalent to $|x^2-4x|+3\geq x^2+|x-5|$ . Now use the definition of the absolute value, $|x-5|=x-5$ if $x>5$ , ... etc.

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