(log16(5))^(log5(1/4)

Question

anonymous · Answer

$$\log_{16} 5^{\log_{5}\frac{ 1 }{ 4 }}$$

anonymous · Answer

Would the 5 and the log 5 cancel out and I somehow end up with 4 because I take 1/4 of 16?

zepdrix · Answer

These rules apply to logs with any base that matches the exponential base.$$\large \ln e^x = x$$$$\large e^{\ln x}=x$$Yah I think you have the right idea :) you can simplify the inside a bit$$\large 5^{\ln_5{1/4}}=\frac{1}{4}$$Giving you a problem of,$$\large \log_{16}{1/4}$$

zepdrix · Answer

Errr it's important to make sure the problem was typed out correctly. With the way you have it written now, it looks like the exponent is being applied to the entire log, which won't allow us to simplify.

If it's just being applied to the 5 though (which is probably the case :D), then we can use this rule.

zepdrix · Answer

16 to what power is 1/4? :D

anonymous · Answer

-1/2?

zepdrix · Answer

Yayyy \:D/

anonymous · Answer

the problem is log with the little 16, and then the big 5.. and that's all raised to the log little 5 and then 1/4. (Sorry that's the best way I can describe it.)

anonymous · Answer

I drew a picture of it: http://i.imgur.com/LGglj.png

zepdrix · Answer

Oh ok, so the exponent is being applied to the 5, and not to the log :D So that's good.