Please help me sort out these questions

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April 25th 2009, 01:14 AM
dave14

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Please help me sort out these questions

Hello,

i am new to the forum; i am glad i found what i have been looking for.
I am just OK with maths; i have been struggling with these few pre-calculus question (some are logarithm); i have attached the questions.. I would really appreciate if anyone of you (maths expert/guru) :) can help me solve these.
Thanks a bunch!! (Bow)

Please check the attached file.
April 25th 2009, 01:46 AM
Soroban

Hello, Dave!

Welcome aboard!

Here's the last one . . .

Quote:

7. Express as the sum or difference of terms.

. . $\log_4\left(\frac{4^x\cdot 4^{2x}\cdot4y}{64}\right)$

We have: . $\log_4\left(\frac{4^x\cdot 4^{2x}\cdot4\cdot y}{4^3}\right) \;=\;\log_4\left(4^{3x-2}\cdot 4y\right)<br /> \;=\;\log_4\left(4^{3x-2}\right) + \log_4(y)$

. . . . . . $= \;(3x-2)\!\cdot\!\underbrace{\log_4(4)}_{\text{This is 1}} \:+\: \log_4(y) \;=\;3x - 2 + \log_4(y)$
April 25th 2009, 05:49 AM
dave14

Quote:

Originally Posted by Soroban

Hello, Dave!

Welcome aboard!

Here's the last one . . .

We have: . $\log_4\left(\frac{4^x\cdot 4^{2x}\cdot4\cdot y}{4^3}\right) \;=\;\log_4\left(4^{3x-2}\cdot 4y\right)<br /> \;=\;\log_4\left(4^{3x-2}\right) + \log_4(y)$

. . . . . . $= \;(3x-2)\!\cdot\!\underbrace{\log_4(4)}_{\text{This is 1}} \:+\: \log_4(y) \;=\;3x - 2 + \log_4(y)$

thanks for the help mate! would appreciate if you can sort out the rest..
April 25th 2009, 09:48 AM
stapel

Quote:

Originally Posted by dave14

thanks for the help mate! would appreciate if you can sort out the rest..

What have you tried? Where are you stuck?

Please be complete, so we can "see" where you're having trouble.

Thank you! (Wink)

Note to other viewers: The text of the exercises is as follows:

Quote:

4) Assume the $3000 investment in problem (3) is placed in an account where interest is compounded continuously. Find the total amount of the investment after five years have passed (assuming no additional deposits or withdrawals) and find the amount of interest earned.

5) Find the time necessary for $500 to grow to $850 when placed in an account that earns 8% compounded semi-annually, assuming no additional deposits or withdrawals. You can certainly solve this graphically or, if you have worked some of the homework problems in section 5.4, you can use the 1-to-1 property of the exponential function and solve this problem algebraically.

6) Explain how the graph of G(X) = -2 * 3^(X + 1) + 1 can be obtained from F(X) = 3^(X) through a series of transformations.

7) Expand and simplify the following logarithmic expression using properties of logarithms, so that it becomes a sum or difference of terms.

. . . . . $\log_4\left[\frac{4^x\, \times\, 4^{2x}\, \times\, 4y}{64}\right]$
April 25th 2009, 11:14 AM
dave14

well i have several questions but these are the ones i am stuck with..would appreciate any help!! thanks
April 25th 2009, 11:30 AM
e^(i*pi)

Quote:

Originally Posted by dave14

well i have several questions but these are the ones i am stuck with..would appreciate any help!! thanks

What does question 3 say? I get the feeling you can't answer 4 without knowing 3.

The compound interest formula is $N(t) = N_0(1+x)^t$ where

$N(t)$ = Amount at time t

$N_0$ = Amount at t=0

$x$ = interest rate (per unit of time)

$t$ = time.

------

5) Use the above formula with
$N(t) = 850$

$N_0 = 500$

$x = 0.08$

$t = t$

$t = \frac{log(\frac{N(t)}{N_0})}{log(1+x)} = \frac{log(N(t)) - log(N_0)}{log(1+x)}$

I get 6.89 six month periods = 3.45 years
April 25th 2009, 11:51 AM
stapel

Quote:

5) Find the time necessary for $500 to grow to $850 when placed in an account that earns 8% compounded semi-annually, assuming no additional deposits or withdrawals. You can certainly solve this graphically or, if you have worked some of the homework problems in section 5.4, you can use the 1-to-1 property of the exponential function and solve this problem algebraically.

Where are you stuck? You took the compound-interest formula, plugged "500" in for "P", "850" in for "A", "0.08" in for "r", and "2" in for "n", and then used whichever method you prefer for solving for the time "t".

Then what?

Please be complete, keeping in mind that we have no idea what was taught in "section 5.4" of whatever book you're using. Thank you! :D
April 26th 2009, 05:01 PM
dave14

Quote:

Originally Posted by stapel

Where are you stuck? You took the compound-interest formula, plugged "500" in for "P", "850" in for "A", "0.08" in for "r", and "2" in for "n", and then used whichever method you prefer for solving for the time "t".

Then what?

Please be complete, keeping in mind that we have no idea what was taught in "section 5.4" of whatever book you're using. Thank you! :D

i am sorry for that; didnt notice that :)! well its the section from COllege Algebra Seventh Edition (logarithm). I still need help with these questions. anyone please.. (Nerd)