ButterflyBlood
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Mon Jan-26-04 01:03 AM
Original message |
help my friend with his math |
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ok, each of these logs is base 3:
log(x+3) + log(x-3) = 2
can anyone figure out x?
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TXlib
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Mon Jan-26-04 01:07 AM
Response to Original message |
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Edited on Mon Jan-26-04 01:36 AM by TXlib
log(x+3) + log(x-3) = log{(x+3)(x-3)} = 2
I assume that's log base 10?
then exponentiate both sides:
10^log{(x+3)(x-3)} = (x+3)(x-3) = 10^2 = 100
x^2 - 9 = 100
x^2 = 109
x = +/- sqrt(109)
On Edit: Whoops, I didn't read your message closely enough...
Use base 3 to exponentiate both sides:
3^log{(x+3)(x-3)} = (x+3)(x-3) = 3^2 = 9
x^2 - 9 = 9
x^2 = 18
x = +/- sqrt(18)
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Waistdeep
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Mon Jan-26-04 01:44 AM
Response to Reply #1 |
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In this problem the negative root would be disallowed because both (x-3) and (x+3) would be negative and the log of a negative number gets you into complex numbers, which I'm sure wasn't intended in this problem.
So the answer is just x = +sqrt(18) = +3 sqrt(2)
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TXlib
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Mon Jan-26-04 08:39 AM
Response to Reply #9 |
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Ahhh, the dangers of mixing tequila and mathematics...
Don't drink and derive.
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onebigbadwulf
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Mon Jan-26-04 01:14 AM
Response to Original message |
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Edited on Mon Jan-26-04 01:57 AM by onebigbadwulf
Okay to add logs you multiply their components
log (a) + log (b) = log (ab)
so log3 (x^2 - 9) = 2
And because we have to work in log 10 we must use the rule
log b (x) = log 10 (x)/ log10 (b)
soooo
log10 (x^2-9)/ log10 (3) = 2
multiply over
log10 (x^2 - 9) = 2 log10 (3)
///////////////////////editted back to original///////
log10 (x^2 - 9) = log10 (3^2)
so x^2 - 9 = 9 x^2 = 18
or x= sqrt 18
GOT IT
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TXlib
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Mon Jan-26-04 01:36 AM
Response to Reply #2 |
6. You were right up til log10 (x^2 - 9) = 2 log10 (3) |
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log10 (x^2 - 9) = 2 log10 (3)
log10 (x^2 - 9) = log10 (3^(1+2))
so x^2 - 9 = 27
x^2 = 36
or x= 6
a logb(c) = logb(c^a), where logb(x) is log base b of x.
so, 2 log10 (3) = log10 (3^2), not log10 (3^(1+2)).
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question everything
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Mon Jan-26-04 01:37 AM
Response to Reply #2 |
7. I think that you are mistaken |
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Let's go to the line where you have everything on the basis of 10:
log10(x^2-9) = 2 log10 (3)
Next should be
log10 (x^2-9) = log10 (3^2), not 3(1+2) as you wrote
thus
log10 (x^2-9) = log10 (9)
x^2 - 9 = 9
x^2 = 18
x = sq root of 18
You can reach the same conclusion without going through the conversion to the basis of 10:
log3(x^2-9) = 2
(x^2-9) = 3^2
x^2 - 9 = 9
x^2 = 18
x = sq root of 18
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onebigbadwulf
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Mon Jan-26-04 01:43 AM
Response to Reply #7 |
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2 log (x) = log (x)^2
and the law of exponents says that bringing an exponent inside brackets means you add them.
so
log (x)^2 = (x^1)^2 = (x^(1+2)) = (x^3)
I roxor
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TXlib
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Mon Jan-26-04 01:50 AM
Response to Reply #8 |
10. OK, let's try your way out with numbers |
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Assume base 10 to make it easy:
5 log 100 = 5 * 2 = 10
According to you, 5 log 100 = (log 100)^5 = 2^5 = 32, if I'm interpreting your brackets right.
The law of exponents says:
a log(b^c) = log(b^(a*c))
not log(b^(a+c)).
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Waistdeep
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Mon Jan-26-04 01:51 AM
Response to Reply #8 |
11. Onebigbadwulf, you're definitely wrong |
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Substitute your x=6 into the original equation
log(x+3) + log(x-3) = 2 log(6+3) + log(6-3) = 2 log(9) + log(3) = 2
since we're working in base 3, log(9) = 2, log(3) = 1
2 + 1 = 2 ??????
sqrt(18) = 3 sqrt(2) is correct.
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onebigbadwulf
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Mon Jan-26-04 01:53 AM
Response to Reply #11 |
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that was my original answer too but it didnt look right
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question everything
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Mon Jan-26-04 01:53 AM
Response to Reply #8 |
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You do not bring an exponent inside a bracket
You X is not an exponent.
thus, the sample above is:
2 log X = log X^2
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TXlib
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Mon Jan-26-04 01:57 AM
Response to Reply #7 |
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if x^2 = 18, then x = +/- sqrt(18)
Don't forget the other root!
(Former physics teacher here...)
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Waistdeep
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Mon Jan-26-04 02:00 AM
Response to Reply #14 |
15. Other root doesn't work |
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See post 9., above
Former physics teacher here, too.
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question everything
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Mon Jan-26-04 03:08 AM
Response to Reply #14 |
17. I don't even care to remember of how many years it has been |
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since I solved such problems, or just used logs in my work ;-)
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onebigbadwulf
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Mon Jan-26-04 01:18 AM
Response to Original message |
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I fixed my post now it's flawless
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Parrcrow
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Mon Jan-26-04 01:19 AM
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DON'T PANIC
the answer is 42. The answer to everything is 42.
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DiverDave
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Mon Jan-26-04 02:51 AM
Response to Reply #4 |
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why go through all that?...42
Dont Panic
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LiberalVoice
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Mon Jan-26-04 01:33 AM
Response to Original message |
5. All these numbers are scarying me! |
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Make it stop mommy! Make it stop!
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DU
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Sun May 05th 2024, 07:01 AM
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