Thread: Help w/ my 1st Calc test!

1. 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

2. 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, $6e^{ln8}=48$

3. $b^x=e^{kx}$

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.

4. 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 $ab=-4$.

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