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#1 2006-01-31 15:40:25

Andrea
Guest

Solving systems of equations with an exponent of x.

Heya, I'm in algebra III/IV, and I'd like help with this problem neither I nor my teacher can figure out.
We've been punching numbers into a graphing calculator and coming up with answers, but I want to know why it works.
We're finding the points where two lines intersect.
The equations of the lines are
y=4(2^x)
y=34.6+17x

I've tried substituting for y, and got stuck at    log(base 2)36.7625x=x
And tried subsituting for x and got stuck at    .018y-logy=.014

How can you "unlogify", as I call it, the logarithms where there are variables on both sides of the equation?

Help would be greatly appreciated, as not being able to figure this out is driving me nuts!
                    -Andrea

#2 2006-01-31 15:59:01

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Solving systems of equations with an exponent of x.

There is no way to (mathematically) explicitly solve for x.  This is the case for many equations.  You can, however, use computer algorithms to approximate a solution.  This is what graphing calculators do.

Oh, and if you didn't know, explicitly solving for x means:

x = ____________

Where that blank does not contain x.  If an equation is not explicit, it is called implicit.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-01-31 16:16:14

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Solving systems of equations with an exponent of x.

Mehehehe... if your in algebra III/IV your in algebra 0.75.

I'm curious, what exactly does one learn in algebra 3 and 4 that you don't learn in calculus? I thought algebra only went as high as 2, then precalc (Aglebra 3?) then calculus and beyond. Didn't know there was algebra 3 and 4. Interesting.


A logarithm is just a misspelled algorithm.

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#4 2006-01-31 16:16:16

Andrea
Member
Registered: 2006-01-31
Posts: 11

Re: Solving systems of equations with an exponent of x.

Ricky wrote:

There is no way to (mathematically) explicitly solve for x.  This is the case for many equations.  You can, however, use computer algorithms to approximate a solution.  This is what graphing calculators do.

Oh, and if you didn't know, explicitly solving for x means:

x = ____________

Where that blank does not contain x.  If an equation is not explicit, it is called implicit.

Oh, thank you!
That must be why the book had nothing about it.
Unsolvable, gotcha.
Thanks muchly.


Black holes are when God divided by zero.

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#5 2006-01-31 16:19:04

Andrea
Member
Registered: 2006-01-31
Posts: 11

Re: Solving systems of equations with an exponent of x.

mikau wrote:

Mehehehe... if your in algebra III/IV your in algebra 0.75.

I'm curious, what exactly does one learn in algebra 3 and 4 that you don't learn in calculus? I thought algebra only went as high as 2, then precalc (Aglebra 3?) then calculus and beyond. Didn't know there was algebra 3 and 4. Interesting.

Haha, .75. Wooh, I must be in the CT class.
I think it's different with different schools. At my school, the first year of algebra is algebra I/II, semesters one and two.
Then you take Geometry.
Then you go back and take algebra III/IV.
I'll be taking pre-calc next year.
I don't understand why we have to split up the algebra classes. I think we could be in precalc already, as a lot of the stuff we've done in algebra this year was just re-learning what we already knew in Algebra 1.
I don't think many people in my class noticed that, though... Many people didn't understand much.


Black holes are when God divided by zero.

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#6 2006-01-31 17:10:33

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Solving systems of equations with an exponent of x.

Many math classes have long periods of learning what you should already know.  This is because math takes practice and you must understand everything you have learned fully to understand more advanced things.

It does get pretty annoying though.  In vector calculus, we learned how to deal with vectors (ironically having nothing to do with calculus).  In multivariable calculus, we spent a month reviewing what we learned in vector calculus, then never used it again.  Finally, in calculus of several variables (even more ironically, the book we are using is called Vector Calculus), we actually use vectors and calculus.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#7 2006-01-31 17:18:37

Andrea
Member
Registered: 2006-01-31
Posts: 11

Re: Solving systems of equations with an exponent of x.

So you're saying that a lot of the junk we're learning that I don't think has anything to do with anything will become useful?
I think we could've skipped the unit about "How to determine if a question is biased."
That seemed like a journalism thing to do...

And I love your signature!


Black holes are when God divided by zero.

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#8 2006-01-31 18:21:44

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Solving systems of equations with an exponent of x.

I read a book on algebra 1, then on 2, then trig, now almost done calculus, in a little over a year. (cause I don't have other subjects to worry about) I'd say all that is pretty unecessary. Though it doesn't hurt.

Hey, Ricky, is multivariable calculus hard? Btw that series of complaints was hilarious!


A logarithm is just a misspelled algorithm.

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#9 2006-01-31 18:26:27

Tigeree
Member
Registered: 2005-11-19
Posts: 13,847

Re: Solving systems of equations with an exponent of x.

ohhh i don't get it cause i'm no good at math sad mad


People don't notice whether it's winter or summer when they're happy.
~ Anton Chekhov
Cheer up, emo kid.

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#10 2006-01-31 18:33:21

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Solving systems of equations with an exponent of x.

What are you good at? :-)


A logarithm is just a misspelled algorithm.

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#11 2006-01-31 18:35:15

Tigeree
Member
Registered: 2005-11-19
Posts: 13,847

Re: Solving systems of equations with an exponent of x.

i don't know ? dunno sad


People don't notice whether it's winter or summer when they're happy.
~ Anton Chekhov
Cheer up, emo kid.

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#12 2006-01-31 18:40:56

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Solving systems of equations with an exponent of x.

Come on think. We're all good at something. I'm good at scaring people away and saying dumb stuff.


A logarithm is just a misspelled algorithm.

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#13 2006-01-31 18:47:45

Tigeree
Member
Registered: 2005-11-19
Posts: 13,847

Re: Solving systems of equations with an exponent of x.

...........um.............. giving thretes.....or maybe not


People don't notice whether it's winter or summer when they're happy.
~ Anton Chekhov
Cheer up, emo kid.

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#14 2006-01-31 19:05:08

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Solving systems of equations with an exponent of x.

threats? :-O Well most tigers are come to think of it.

Last edited by mikau (2006-01-31 19:05:28)


A logarithm is just a misspelled algorithm.

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#15 2006-01-31 19:13:18

Tigeree
Member
Registered: 2005-11-19
Posts: 13,847

Re: Solving systems of equations with an exponent of x.

oh sorry ........um............. climbing maybe hmm


People don't notice whether it's winter or summer when they're happy.
~ Anton Chekhov
Cheer up, emo kid.

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#16 2006-01-31 20:26:44

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Solving systems of equations with an exponent of x.

Tiger, tiger, burning bright
In the forests of the night,
What immortal hand or eye
Framed thy fearful symmetry?

- Rudyard Kipling (author of The Jungle Book)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#17 2006-01-31 20:40:26

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Solving systems of equations with an exponent of x.

sweet!


A logarithm is just a misspelled algorithm.

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#18 2006-02-01 09:35:47

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Solving systems of equations with an exponent of x.

Hey, Ricky, is multivariable calculus hard?

If you have a very good understanding of derivatives, integration (especially finding the limits of integration), and understanding how to apply these, then no.

The only other thing to consider are converging and diverging series, but for those, all you have to do is memorize a few different tests to see which is which.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#19 2006-02-01 14:14:38

Andrea
Member
Registered: 2006-01-31
Posts: 11

Re: Solving systems of equations with an exponent of x.

I like the poem, maths, but I noticed that eye and symmetry don't rhyme...

I think calculus sounds fun! A lot of the stuff we do in my math class is just plugging things into formulas we learned two years ago. I'm ready to learn something new.
Bwahahaa.
I want to get through AP Calculus III/IV before graduating highschool. WOOH! That class will be AWESOME!


Black holes are when God divided by zero.

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#20 2006-02-01 18:19:33

Tigeree
Member
Registered: 2005-11-19
Posts: 13,847

Re: Solving systems of equations with an exponent of x.

MathsIsFun wrote:

Tiger, tiger, burning bright
In the forests of the night,
What immortal hand or eye
Framed thy fearful symmetry?

- Rudyard Kipling (author of The Jungle Book)

the jungle book up cool cool

Tigeree now wink


People don't notice whether it's winter or summer when they're happy.
~ Anton Chekhov
Cheer up, emo kid.

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