# Logs

• May 31st 2007, 05:33 PM
Jimgotkp
Logs
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, 05:41 PM
ThePerfectHacker
Quote:

Originally Posted by Jimgotkp
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

$\log \sqrt[4]{\frac{x}{y}} = \log \left(\frac{x}{y}\right)^{1/4} = \frac{1}{4} \log \frac{x}{y} = \frac{1}{4}\log x - \frac{1}{4}\log y$
• May 31st 2007, 05:43 PM
Jimgotkp
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, 05:50 PM
Krizalid
But post all exercises that you can't solve. :)
• May 31st 2007, 06:02 PM
Jimgotkp
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, 06:44 PM
Jonboy
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.

Quote:

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

2. $\ln \frac{{\sqrt[3]{x}}}{{\sqrt[3]{y}}}$
Since $log_{b}a\,-\,log_{b}c\,=\,log_{b}\frac{a}{c}$, Problem # 2 can be rewritten as $ln{\sqrt[3]{x}}\,-\,ln{\sqrt[3]{y}}$

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3. $\frac{1}{3}logx$
A rule says: $x\,log_{b}\,a\,=\,log_{b}\,a^{x}$

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

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4. $4\,log(x\,-\,1)\,+\,2\,log(\,x\,+\,4)$
Using the previous rule, we can rewrite this as: $log(x\,-\,1)^{4}\,+\,log(\,x\,+\,4)^{2}$

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

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5. $\frac{1}{2}log_{a}(x\,-\,3)\,-\,\frac{1}{3}log_{a}(x\,+\,3)$
Move the fraction: $log_{a}(x\,-\,3)^{\frac{1}{2}}\,-\,log_{a}(x\,+\,3)^{\frac{1}{3}}$
Once again,.. $log_{b}a\,-\,log_{b}c\,=\,log_{b}\frac{a}{c}$: .... $log_{a}\frac{(x\,-\,3)^{\frac{1}{2}}}{(x\,+\,3)^{\frac{1}{3}}}$
• May 31st 2007, 06:55 PM
Jimgotkp
sorry moderator, i didnt see the rules before.

jonboy, thank you very much. im just trying to clarify the answers up.
• May 31st 2007, 07:03 PM
Jhevon
Quote:

Originally Posted by Jimgotkp
sorry moderator, i didnt see the rules before.

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.

Quote:

Originally Posted by Jimgotkp
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.)

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

Quote:

6. 1/4log b(x+2) - 1/5log b(3-x)
$\frac {1}{4} \log_{b} (x + 2) - \frac {1}{5} \log_{b} (3 - x) = \log_{b} (x + 2)^{ \frac {1}{4}} - \log_{b} (3 - x)^{ \frac {1}{5}}$

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

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