square root in a log: log_5(sqrt(5))/log_5(10th-rt(5))

[letsgetaway]

Solve. a = 10 and b = 5

I'm not sure what to do with this problem. The denominator really has me confused with the 10 in front of the square root of 5. Can anyone give me a clue how to solve this? :idea:

My guess is that I should take the square root in the numerator and move it to the beginning of the log. As for the denominator, I don't know.

log 5 5^1/2
-------------------------------
log 5 ^10 sqrt(5)

=

1/2 log 5
----------
10 + 1/2 log 5 5

 

[pka]

Look at the image that you posted.
Is it correct? You don't seem to be talking about it.

Here is what that image equals.
\(\displaystyle \L
\frac{{\log _b \sqrt b }}{{\log _b \sqrt[a]{b}}} = \frac{{\frac{1}{2}}}{{\frac{1}{a}}}\)

 

[letsgetaway]

WOW! I can't believe I missed this question. Thanks. Now I understand. Sometimes I think too hard. Yes, the image is correct. I was just taking the wrong approach to the problem.