Help w/ my 1st Calc test!

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September 28th 2009, 11:00 AM
TodaYou

Help w/ my 1st Calc test!

Not actually homework, rather sample problems that will be on my test tomorrow. Professor didn't give us the answers to the practice problems (State school...) so I don't know if they're right or not. I haven't taken a real math class since high school so a lot of this is foreign to me. Anyway....

1. Given Ln A = 10, solve ln(Ae^3)
$ lnA+lne^3 = 10 + 3lne = 10 + 3 = 13 $

2. (ln64-ln8)/ln2
$ (ln64-ln8^2)/ln2^5 = (ln64-2ln8)/5ln2 = (64-2(8))/(5*2) = 48/10 $

3. Given e^A = 6, solve e^(A+ln8)
$ (e^A)(e^ln8) = 6(e^ln8) = ???? I don't know what to do... $

And there are two that I don't even know how to start

7. If b^x = e^(kx), solve for k in terms of b.

8. Find k such that 2^(-x/5) = e^(kx) for all x.

Also, how would I factor something like x^2+3x-4???

I don't have any problem with limits because I go to class and that's what he has been teaching, however this test has a lot of algebra on it and I haven't even done an algebraic equation in 4 years. I'm know it's easy math and it's frustrating because I could do this in high school, but now I'm in the dark. Help is greatly appreciated please/thank you
September 28th 2009, 12:37 PM
adkinsjr

Quote:

Originally Posted by TodaYou

Not actually homework, rather sample problems that will be on my test tomorrow. Professor didn't give us the answers to the practice problems (State school...) so I don't know if they're right or not. I haven't taken a real math class since high school so a lot of this is foreign to me. Anyway....

1. Given Ln A = 10, solve ln(Ae^3)
$ lnA+lne^3 = 10 + 3lne = 10 + 3 = 13 $

2. (ln64-ln8)/ln2
$ (ln64-ln8^2)/ln2^5 = (ln64-2ln8)/5ln2 = (64-2(8))/(5*2) = 48/10 $

3. Given e^A = 6, solve e^(A+ln8)
$ (e^A)(e^ln8) = 6(e^ln8) = ???? I don't know what to do... $

And there are two that I don't even know how to start

7. If b^x = e^(kx), solve for k in terms of b.

8. Find k such that 2^(-x/5) = e^(kx) for all x.

Also, how would I factor something like x^2+3x-4???

I don't have any problem with limits because I go to class and that's what he has been teaching, however this test has a lot of algebra on it and I haven't even done an algebraic equation in 4 years. I'm know it's easy math and it's frustrating because I could do this in high school, but now I'm in the dark. Help is greatly appreciated please/thank you

The first problem is correct. I don't understand what you did with the second problem. For the third:

$e^{A+ln8}=e^Ae^{ln8}=6e^{ln8}$

One property of exponential functions is $a^{log_a(x)}=x$

Therefore, $6e^{ln8}=48$
September 28th 2009, 12:42 PM
adkinsjr

$b^x=e^{kx}$

The trick here is to take the logartim of both sides:

$ln(b^x)=ln(e^{kx})$

$xln(b)=kxln(e)$

$xln(b)=kx$

$ln(b)=k$

Try to use this same approach on your problem #8.
September 28th 2009, 12:49 PM
adkinsjr

To factor quadratic functions, notice the pattern:

$(x+a)(x+b)=x^2+ax +bx +ab = x^2 + x(a+b) +ab$

The trick is to find numbers $a,b$ such that $a+b=3$ and $ab=-4$ .

$x^2+3x-4=(x+4)(x-1)$