Can someone check my answers please?

[m0286]

From your guys help, THANKS I was able to understand questions better I was hoping someone would check my answers:

for : evaluate the following logarithms:
log22^log55 I got:
log22=2^1 log55=5^1
=1 =1
therefore 1^1=1 is that correct???

Another one: solve the following logarithm equation:
log25=log2(x+32)-log2x
I got:
log25=log2(x+32)-log2x
5=log2 (x+32)/x
x+32=(5)(x)
x+32-5x
4x-32=0
x-8
therefore x=8.... is that right??????

Next: Determine the deriviative of the following functions:
d) y=2x^3 e^4x
well I figured out how to do the e^4x part it would be: 4e^4x so would the derivative be 6x^2 4e^4x????

e.) determine the derivative:
y=sq root(x^3+e^-x +5) I got:...
y=(x^3 + e^-x + 5)^1/2
dy/dx= 1/2 (x^3 + e^-x + 5)^-1/2 (3x^2-1e^-x) Now Im stuck... Is what I have right soo farr and if so can someone help me to continue.

[whozum]

From your guys help, THANKS I was able to understand questions better I was hoping someone would check my answers:

for : evaluate the following logarithms:
log22^log55 I got:
log22=2^1 log55=5^1
=1 =1
therefore 1^1=1 is that correct???

Correct, but your reasoning isnt right.

log_22 = 1,\ not \ 2^1.
2^{log_22} = 2 because [itex] log_22 = 1[/tex]

Another one: solve the following logarithm equation:
log25=log2(x+32)-log2x
I got:
log25=log2(x+32)-log2x
5=log2 (x+32)/x
x+32=(5)(x)
x+32-5x
4x-32=0
x-8
therefore x=8.... is that right??????

Hard to read your logs, I'm interpreting it as:

log_25 = log_2(x+32)-log_2x which simplifies to
log_25 = log_2\left(\frac{x+32}{x}\right)

I'm not sure what you did here, but what your supposed to do is exponentiate both sides with base 2.

2^{log_25} = 2^{log_2\left(\frac{x+32}{x}\right)} and you'll see the log's cancel out and you get:

5 = \frac{x+32}{x} which you did get.

From there use some algebra to solve for x, you did correctly.


Next: Determine the deriviative of the following functions:
d) y=2x^3 e^4x
well I figured out how to do the e^4x part it would be: 4e^4x so would the derivative be 6x^2 4e^4x????


Don't forget the product rule. You differentiated each term correctly though.

e.) determine the derivative:
y=sq root(x^3+e^-x +5) I got:...
y=(x^3 + e^-x + 5)^1/2
dy/dx= 1/2 (x^3 + e^-x + 5)^-1/2 (3x^2-1e^-x) Now Im stuck... Is what I have right soo farr and if so can someone help me to continue.

This is all correct except you differentiated [itex] \frac{1}{e^x} [/tex] Incorrectly. Choose u = e^x and apply the chain rule.