The question is

log_{2}(x+1)≤3

thena<x≤b.

What areaandb?

How do I solve this?

I can solve for b which is 7. But how do I solve for a?

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- Jul 24th 2009, 03:48 AMshrrikeshInequality with logarithm help needed.
The question is

**log**_{2}(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? - Jul 24th 2009, 04:01 AMMoo
Hello,

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

So 1+x has to be > 0

This makes x>-1 (a=-1)

Then, we know that the logarithm is an increasing function.

So $\displaystyle \log_2(1+x)\leq 3 \Leftrightarrow 1+x \leq 2^3$

so b=... - Jul 24th 2009, 04:15 AMshrrikesh
Thanks.

I didn't know that.