# Thread: Solving a logarithmic inequality.

1. ## Solving a logarithmic inequality.

Hello,

I would like to ask how this inequality :

$\displaystyle (ln{2})^{n}<\frac{0.02(1-ln{2})}{2^{-0.5}-0.5}$

results to this inequality:

$\displaystyle n>\frac{ln{(\frac{0.02(1-ln{2})}{2^{-0.5}-0.5})}}{ln({ln{2})}}$

I am working on it for quite long now and I cannot justify why it changed from smaller to bigger, I find that n is smaller not bigger.

Thank you!

2. ## Re: LOGARITHMIC INEQUALITY RESULT [don't understand]

$\displaystyle ln(ln(2))$ is negative, so when you divide through by it, the inequality sign changes.

3. ## Solved

Hi there!

Sad to say.. but I didn't know that! I had to check it out and you are right it is negative because 2<e.

Thank you very much for the solution, helped me alot!

Bye!

4. ## Re: Solved

Originally Posted by Melsi
Hi there!

Sad to say.. but I didn't know that! I had to check it out and you are right it is negative because 2<e.
actually, because $\displaystyle \ln{2} < 1$