Evaluating Logs & Derivatives: More Questions Answered Here

[m0286]

Can some one check my answers please?

The answers are in my reply post at the bottom of this page THANKS


I have a couple more log questions I am stuck on. They keep giving me log questions that they never showed me how to do.. very fustrating!
I need to evaluate the following logarithms:

68 a). log22^log55
I don't even know where to begin.. I never done a log with an exponent log?

69. log25=log2(x+32)-log2x

Determine the derivative of:
70 c) y= 2x^3 e^4x

e) y= square root(x^3 + e^-x +5)
I know this one should probably go to. (x^3 + e^-x +5)^1/2... then,
dy/dx= (x^3 + e^-x +5)^1/2 * 1/2(x^3 + e^-x +5)^-1/2 * (3x^2)now I am confused? does the e^-x have a derivative?? like -xe^-2?? i got no idea.
CAN ANYONE HELP ME PLEASE...
THANKZ YA!

 

[Jameson]

For part a, is that

(\log_{2}2)^{\log_{5}5} or \log_{2}(2)^{\log_{5}5}?

 

[m0286]

umm there are no brackets, but i think the 2 is in part with the log2

 

[Pyrrhus]

Hrm

\log_{5} 5 = 1

5^1 = 5

log_{2} 5= log_{2} (x+32) - log_{2} x

log_{2} 5= log_{2} \frac{x+32}{x}

5 = \frac{x+32}{x}