# Thread: Logarithmic Inequalities

1. ## Logarithmic Inequalities

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.

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

3. Originally Posted by FernandoRevilla
Use that the inequality $\displaystyle \log_3 y\geq 0$ is equivalent to $\displaystyle y\geq 1$
Thanks for your reply but i want to know how to get rid of modulus...

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