Comparing Two Logarithms Base 10

Hi all ---

For this multiple choice question, I don't know how to compare (a) and (b).

http://i56.tinypic.com/28wot1z.jpg

I try ---

Then ---

or if I sub in L ---

Squaring both sides ---

Because --- squaring this for the 1st and then multiplying by 2 for the 2nd --- and .

__1st Question ---__ But how can I compare the last two inequalities? I don't know what specifically L is?

__2nd Question ---__ How does solution get ?

Thanks a lot ---

Re: Comparing Two Logarithms Base 10

simplified choices in terms of L ...

(a) (b) (c) (d)

for (a) and (b) ...

because

finally, since , both (c) and (d) are > 1 > L ... you don't need to compare them against each other.