Thread: logs, growth, decay, halflife help!!!!!

1. logs, growth, decay, halflife help!!!!!

Determine the value of x without a calculator and show your work.

1) ln(2x-1)+ln(3x-2)=ln7 (i did this but i want to check my answer)
2) ln(x-1)-ln(x-3)=1 (i did this dont need help anymore but if i can check answers)
3) (2e^x)(x^2) - (e^x)x=e^x (did this too)
4) xlnx - x = 0 (did this too)

and some growth and decay problems show your work

5) How long does it take an amount of money to double, if it is deposited at 6% compounded continuously? (I did this too want to check answer)

8) Determine the value of a CD (certificate of deposit) in the amount of \$10,000 that matures in 8 years and pays 10% per year compounded as indicated.
A) Annually.
B) continuously

2. for xlnx-x=0 take out an x so : x(lnx-1)=0 so by this the roots are x=0 and x=e

lne=1 by the way; they are inverses

for 1. use the muliplication/addition rule for natural logs so that becomes :ln((2x-1)(3x-2))=ln7 and raise them both to the power of e so you get (2x-1)(3x-2)=7. I think you can take it from here.

for 2, use the division/subtraction rule for natural logs. clue: ln ((x-1)/(x-3))=1. repeat steps from above

for 3: x^2*2e^x=e^x*(1-x) (subtract e^x on other side and factor it out) then you can divide both sides by e^x so you have 2x^2=(1-x). You can solve from here

P.S. it looks like your trying to get us to do your whole homework for you. Instead of waiting for an answer try to finish the work yourself. Just getting an answer is not enough. Understanding the material itself is what is important. Sometimes you run into holes and can't figure it out. Spend an hour or so and if your having trouble, ask a few questions. This seems a little ridiculous

3. im still lost with #2 i think im on the wrong track but here is what i got so far
x-1 = ex-3e

4. im being tested on these material, it would be stupid for me if i just get the answer, getting the answer only = wont be able to understand how to solve the problem, anyone can take a calculator and punch in numbers and get an answer.

5. Originally Posted by tjnguyen
im still lost with #2 i think im on the wrong track but here is what i got so far
x-1 = ex-3e
Hi tjnguyen,

2) ln(x-1)-ln(x-3)=1 (i did this dont need help anymore but if i can check answers)
$\ln (x-1)-\ln (x-3)=1$
$\ln \frac{x-1}{x-3}=1$
$\frac{x-1}{x-3}=e^1$ by definition.
$x-1=ex-3e$ which is what you have so far.
$x-ex=1-3e$ since you are solving for x.
$x(1-e)=1-3e$
$x=\frac{1-3e}{1-e}$

6. ok thanks thats what i got for #2 but mine goes like this

-3e+1/1-e or -3e+1/-e+1

i can use either or right and the one you gave me, also how do i set it up like the way u did it, with the math codes?

7. Originally Posted by tjnguyen
ok thanks thats what i got for #2 but mine goes like this

-3e+1/1-e or -3e+1/-e+1

i can use either or right and the one you gave me, also how do i set it up like the way u did it, with the math codes?
Yes either is fine.

And the math codes are done using LaTeX. There's a sub-forum here with help for beginners.