# More log questions.

## Main Question or Discussion Point

I have a couple more log questions Im 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 dont 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 im confused??? does the e^-x have a derivative?? like -xe^-2?? i got no idea.
THANKZ YA!

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For part a, is that

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

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

Pyrrhus
Homework Helper
Hrm

$$\log_{5} 5 = 1$$

$$5^1 = 5$$

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

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

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

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