# Logarithmic Inequalities

• May 25th 2011, 09:27 PM
PranavArora
Logarithmic Inequalities
I am doing a lot of questions on logarithmic inequality but i am stuck at one question:-

http://i54.tinypic.com/2uo75mb.png

I dont from where to start.
• May 25th 2011, 09:36 PM
FernandoRevilla
Use that the inequality $\log_3 y\geq 0$ is equivalent to $y\geq 1$
• May 25th 2011, 10:33 PM
PranavArora
Quote:

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...
• May 26th 2011, 12:08 AM
FernandoRevilla
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.