Solving systems of equations with an exponent of x.

Andrea · 2006-01-31 15:40:25

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

Ricky · 2006-01-31 15:59:01

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.

mikau · 2006-01-31 16:16:14

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.

Andrea · 2006-01-31 16:16:16

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.

Andrea · 2006-01-31 16:19:04

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.

Ricky · 2006-01-31 17:10:33

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.

Andrea · 2006-01-31 17:18:37

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!

mikau · 2006-01-31 18:21:44

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!

Tigeree · 2006-01-31 18:26:27

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

mikau · 2006-01-31 18:33:21

What are you good at? :-)

Tigeree · 2006-01-31 18:35:15

i don't know ?

mikau · 2006-01-31 18:40:56

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

Tigeree · 2006-01-31 18:47:45

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

mikau · 2006-01-31 19:05:08

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

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

Tigeree · 2006-01-31 19:13:18

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

MathsIsFun · 2006-01-31 20:26:44

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)

mikau · 2006-01-31 20:40:26

sweet!

Ricky · 2006-02-01 09:35:47

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.

Andrea · 2006-02-01 14:14:38

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!

Tigeree · 2006-02-01 18:19:33

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 cool

Tigeree now

Math Is Fun Forum

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

Solving systems of equations with an exponent of x.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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