Directions: use the properties of logarithms to write the expression as a sum, difference, or multiples of logarithms of x, y, or constant.

log (4th root of (x/y))

thanks for your help. i appreciate it

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- May 31st 2007, 04:33 PMJimgotkpLogs
Directions: use the properties of logarithms to write the expression as a sum, difference, or multiples of logarithms of x, y, or constant.

log (4th root of (x/y))

thanks for your help. i appreciate it - May 31st 2007, 04:41 PMThePerfectHacker
- May 31st 2007, 04:43 PMJimgotkp
wow thanks for those fast replies. i was trying to ask my friends in ap calc, and they totally forgot how to do it.

THANK YOU!

have a math quiz on this stuff tomorrow :( - May 31st 2007, 04:50 PMKrizalid
But post all exercises that you can't solve. :)

- May 31st 2007, 05:02 PMJimgotkp
okay here is a list of log problems so that i can check it later tonight.

Use the properties of logarithms to write the expression as a sum, difference, or multiples of logarithms of x, y, constants.

1. log1000x4 <-(x to the 4th. i dont have those programs to write perfect math problems, sorry.)

2. In(3rd root of x) / (3rd root of y)

3. 1/3logx

4. 4log(x-1) + 2log(x+4)

5. 1/2log a(x-3) - 1/3log a(x+3)

6. 1/4log b(x+2) - 1/5log b(3-x) - May 31st 2007, 05:44 PMJonboy
Hi Jimgotkp! I helped with 2,3,4 and half of 5. You all check and make sure I didn't make any mistakes because I have to get off the comp.

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Use the properties of logarithms to write the expression as a sum, difference, or multiples of logarithms of x, y, constants.

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2. $\displaystyle \ln \frac{{\sqrt[3]{x}}}{{\sqrt[3]{y}}}$

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3. $\displaystyle \frac{1}{3}logx$

so you can rewrite this is as: $\displaystyle log\,x^{\frac{1}{3}}$. I don't see how you can simplify this further.

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4. $\displaystyle 4\,log(x\,-\,1)\,+\,2\,log(\,x\,+\,4)$

Then as a multiple: $\displaystyle \log [(x - 1)^4 (x + 4)^2]$

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5. $\displaystyle \frac{1}{2}log_{a}(x\,-\,3)\,-\,\frac{1}{3}log_{a}(x\,+\,3)$

Once again,..$\displaystyle log_{b}a\,-\,log_{b}c\,=\,log_{b}\frac{a}{c}$: .... $\displaystyle log_{a}\frac{(x\,-\,3)^{\frac{1}{2}}}{(x\,+\,3)^{\frac{1}{3}}}$ - May 31st 2007, 05:55 PMJimgotkp
sorry moderator, i didnt see the rules before.

jonboy, thank you very much. im just trying to clarify the answers up. - May 31st 2007, 06:03 PMJhevon
lol, i'm not a moderator!

are you sure these are the instructions for all the questions? some of these are already in the form you are asking us to put them in, it would be a better exercise to combine them rather than express them as sums and whatnot. i'll do the ones Jonboy left out.

$\displaystyle \log 1000x^4 = \log 1000 + \log x^4 = 3 + 4 \log x$ .......i assumed we are dealing with log to the base 10 here, so that's why i got the 3

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6. 1/4log b(x+2) - 1/5log b(3-x)

$\displaystyle = \log_{b} \sqrt [4] {x + 2} - \log_{b} \sqrt [5] {3 - x}$

$\displaystyle = \log_{b} \left( \sqrt [4] {x + 2} \sqrt [5] {3 - x} \right)$

if you have any questions, please feel free to ask