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Mathematics Fortress Zone; ...for all ye mathematicians on TTFF!
Topic Started: Jan 15 2013, 12:12 PM (70 Views)
Pooka
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Who is Pooka?

Ok, I thought this idea would be good. Though I don't know exactly where this would go, I'm guessing I should stick it to the general discussions topic, for now.

Anyways, you're here to solve equations others having troubles with, as well as explain them some rules, lessons, etc. Or discuss anything regarding math (that is not math hate, FYI).

For example, this equation came up in today's algebra exam. When I first looked at it, I thought to myself, I'm doomed. The goal is to get the unidentified number X.

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Out of all methods I've learnt in algebra, I couldn't solve this.
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Tails-san
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Ok... Let me get some of it simplified.

(5 cubed)**9 * (5 cubed)**3x = 8 x (2 squared)**2x

That's as far I can get without paper. Also I'm a year below this so I doubt I can fully solve it :P
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AugieD
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"I wanna fly high!"

Are you learning trig?
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Pooka
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Who is Pooka?

@Tails-san, that's exactly the first step I've done. Even then, I couldn't force it into a look I know that lets me solve it.
And @Augie, no, I'm trying to find the number that represents the X.
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AugieD
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"I wanna fly high!"

Cause you have to do trig to solve this. :P
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Pooka
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Who is Pooka?

Until now, a friend told me that I have to take the log of both sides.

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Because what you have to do is take the log of both sides, so what you do is: write log in front of the two words. Then you bring the exponent for the left side in front of the left log, and then the exponent of the right side in front of the right log. Then you divide one log by the other and solve for x


And so far, I don't even know how to get the log out of something. The log is something I'm going to learn as far as I'm concerned next term.
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Pooka
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Who is Pooka?

I think I learnt the logarithms, and that I'm not taking any more of it in the finale 12th grade. However, would somebody show me how to solve this thing step by step in math? Because I think I ruined it.

The kicker, however, is that despite not solving this question fully, I got the full mark in algebra. Weird, huh? :P
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Scientific Tails
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Dancing at the moment, please leave a message

Ok, so the problem with conventional simplification (which I looked into for a step or two before choosing the right way) in this problem is that you need to get everything into the exponents to use the logging both sides trick.

(3√5)9+3x = (1/2)-3(√2)2x
(5)3+x = (2)3(√2)2x
(5)3+x = (2)3+x
ln[(5)3+x] = ln[(2)3+x]
(3+x)ln(5) = (3+x)ln(2)
3ln(5) + xln(5) = 3ln(2) + xln(2)
x(ln(5)-ln(2)) = 3(ln(2)-ln(5))
x(ln(5)-ln(2)) = -3(ln(5)-ln(2))
x = -3

Should be right; works when I plug it in.
Edited by Scientific Tails, Mar 31 2013, 06:51 PM.
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