# Inequality with logarithm help needed.

• July 24th 2009, 03:48 AM
shrrikesh
Inequality with logarithm help needed.
The question is
log2(x+1)≤3

then a<x≤b.

What are a and b?

How do I solve this?

I can solve for b which is 7. But how do I solve for a?
• July 24th 2009, 04:01 AM
Moo
Hello,

The logarithm (in any base) is defined only over $(0,\infty)$

So 1+x has to be > 0
This makes x>-1 (a=-1)

Then, we know that the logarithm is an increasing function.
So $\log_2(1+x)\leq 3 \Leftrightarrow 1+x \leq 2^3$

so b=...
• July 24th 2009, 04:15 AM
shrrikesh
Thanks.
I didn't know that.