# HW problem

1. Dec 21, 2004

### 01

Here's the question:

Simplify the following as much as possible:

ln 5th Sqrt of y^2

a> 2/5 ln y

b> -3 + ln y

c> 3 + ln y

d> 5/2 ln y

A,B,C, or D, which is it?

Last edited: Dec 21, 2004
2. Dec 21, 2004

### assyrian_77

You can write the 5th sqrt of y^2 as y^(2/5) ....... knowing that, it should be easy to get the right answer

3. Dec 21, 2004

### 01

I'm wanting to say "A", correct?

4. Dec 21, 2004

### Popey

Yeap!

...........

5. Dec 21, 2004

### 01

Thanks for the input, now for another, I'm pretty sure of my answer I just want to be sure. Here it is:

Solve the following equation

log(base)5(x - 1) = -1

a> 6

b> 0.2

c> 1.2

d> 0.8

My initial calculations (if they could be called that) came up with C, is that it?

6. Dec 21, 2004

### 01

Here's another while I'm at it:

Suppose you have $6000, how much does a return of 3.25% compounded quarterly for 5 years yield? a> 6195 b> 7040.47 c> 6975 d> 7054.06 I'm wanting to say "B", but am unsure, any help? 7. Dec 23, 2004 ### 01 ***bump*** 8. Dec 23, 2004 ### dextercioby Well,it's right: $$5^{\log_{5}(x-1)}=5^{-1}\Rightarrow x-1=\frac{1}{5}\Rightarrow x=\frac{6}{5}=1.2$$ Here's another while I'm at it: Suppose you have$6000, how much does a return of 3.25% compounded quarterly for 5 years yield?

a> 6195

b> 7040.47

c> 6975

d> 7054.06

I'm wanting to say "B", but am unsure, any help?

So the interest is 3.25% per quarter of the year (trimester)??It means 13% per year.That means 780$per year,which is 3900$ per 5 yrs.

If the interest is 3.25% per year,then it's 4 times less:975$per 5 years,bringing it to a total of 6975$.Answer c).

In this case,what the hell means "compounded quarterly"??Capitalization once every three months???In this case,the rate per trimester is 3,25%/4=0.8125%.For the first trimester it would be 48.75$.Then for the second semester it would be:6048,75$*0.8125%=49.14609375$.So the total for 6 months would be:6097,89609375$.And for the third semester it would be 6097,89609375$*0.8125%=49.5454057617...$(the calcuator gave me only 10 decimals instead of 14).And the procedure would go on.
I don't know what the final result will be,but definitely it is weird.

Daniel.

9. Dec 23, 2004

### Gamma

This is how do it. Develope a simple equation.
First Quarter: $$R1 = (6000 + \frac {0.8125}{100} 6000) = 6000(1+ \frac{0.8125}{100})$$

For the second Quarter: $$R2 = (R1 + \frac {0.8125}{100} R1) = R1(1+ \frac{0.8125}{100}) = 6000(1+ \frac{0.8125}{100})^2$$

There are 20 quarters in 5 years.
So the return after 5 years R20, is given by

$$R20 = 6000(1+ \frac{0.8125}{100})^{20}$$

This gives \$ 7054.05 (d)

Regards,

Gamma.

10. Dec 29, 2004

### jaycob1997

Another approach to this problem is to use the formula for changing the base, which is:

Log(base x)N=(Log(base 10)N)/(Log(base 10)x).

This can be very useful in any future quizzes or exams that you may have. This is also applicable for Ln (which is Log(base e)), e=2.7182...

Applying this formula to your original problem, the equation would look like this:

Log(base 5)(x-1)=-1
(Log(base 10)(x-1))/(log(base 10)5)=-1

Note: Log(base 10)=Log,
futher simplifying, we get

Log(x-1)=-1*Log5

Using properies of logarithms, we get Log(x-1)=Log(5^-1),
take the anti-logarithm of both sides we get, x-1=1/5

therefore answer is: x=1+1/5 or 1.2

PS: Can someone help me with my thread (Supplementary angles for Spherical triangles)??

Last edited: Dec 29, 2004