Trying to solve an equation I thought of.

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May 9th 2011, 10:43 AM
Mathmagician

Trying to solve an equation I thought of.

This is my first time trying to post images and have had horrible luck, so the best I can do is just post the link to my photobucket picture. I had much difficulty fighting with the coding commands on this forum, so I created this from word.

Anyway, when I took pre-calculus algebra (aka college algebra), it seemed like concepts were always presented to us in easily-solvable forms, which rarely yielded ugly numbers.

I came up with this equation and am curious as to how it can be solved. Although I'm sure the algebra is a complete mess on this, does this problem require anything more than algebra (aka calculus, differential equations, etc.)? I just completed calculus 2 and have no idea how to tackle this problem, other than graphing it to find a decimal approximation at x-intercepts.

Is it possible to solve this equation getting exact numbers (aka fractions and logarithms without variables in them)? Or are there some equations that just cannot be solved with exact answers (and I'm referring to equations with one variable, not differential equations). I'm eager to see how this equation could be solved. Thanks.

Here is the link to this equation (again I wish I could post it here, but I haven't been able to):

NOTICE: the 13/7 inside the root is taken to the 0.13x power, not 13 taken to that power then divided by 7.

UnsolvableEquation.jpg picture by b4bis91 - Photobucket
May 9th 2011, 08:12 PM
CaptainBlack

Quote:

Originally Posted by Mathmagician

This is my first time trying to post images and have had horrible luck, so the best I can do is just post the link to my photobucket picture. I had much difficulty fighting with the coding commands on this forum, so I created this from word.

Anyway, when I took pre-calculus algebra (aka college algebra), it seemed like concepts were always presented to us in easily-solvable forms, which rarely yielded ugly numbers.

I came up with this equation and am curious as to how it can be solved. Although I'm sure the algebra is a complete mess on this, does this problem require anything more than algebra (aka calculus, differential equations, etc.)? I just completed calculus 2 and have no idea how to tackle this problem, other than graphing it to find a decimal approximation at x-intercepts.

Is it possible to solve this equation getting exact numbers (aka fractions and logarithms without variables in them)? Or are there some equations that just cannot be solved with exact answers (and I'm referring to equations with one variable, not differential equations). I'm eager to see how this equation could be solved. Thanks.

Here is the link to this equation (again I wish I could post it here, but I haven't been able to):

NOTICE: the 13/7 inside the root is taken to the 0.13x power, not 13 taken to that power then divided by 7.

UnsolvableEquation.jpg picture by b4bis91 - Photobucket

Unless this has been set up deliberately to have a nice root I doubt it can be addressed anyway but numerically (there is also a distinct chance that there is no solution, but I won't be checking)

CB
May 9th 2011, 09:05 PM
topsquark

Quote:

Originally Posted by Mathmagician

I came up with this equation and am curious as to how it can be solved. Although I'm sure the algebra is a complete mess on this, does this problem require anything more than algebra (aka calculus, differential equations, etc.)? I just completed calculus 2 and have no idea how to tackle this problem, other than graphing it to find a decimal approximation at x-intercepts.

I'm with CaptainBlack here. In general if you have something like
$log_{5x}(\text{something}) + Ax^{\text{whatever}} = B$

bet that it cannot be solved analytically. And your equation is muchly much much worse (as Dr. Seuss might say.)

-Dan
May 10th 2011, 07:52 AM
Mathmagician

Thank you, both. I was always wondering whether or not any algebraic equation could be solved analytically. In college algebra, we never covered (and haven't as of calculus 2) logarithms with variable bases. So is there no analytical way of solving for variables in the base of logarithms, or can it only be done for simple examples?

Just out of curiosity, could this equation be solved analytically if the base and the argument of the logarithms were switched? Or is there still way too much algebra to do this analytically?
May 10th 2011, 11:14 AM
topsquark

Quote:

Originally Posted by Mathmagician

Thank you, both. I was always wondering whether or not any algebraic equation could be solved analytically. In college algebra, we never covered (and haven't as of calculus 2) logarithms with variable bases. So is there no analytical way of solving for variables in the base of logarithms, or can it only be done for simple examples?

Just out of curiosity, could this equation be solved analytically if the base and the argument of the logarithms were switched? Or is there still way too much algebra to do this analytically?

The simple examples can still be fairly complicated, but there are only a few "classes" of problems that can be done. The more complicated problems involve reducing the problem to one of the classes. One of the problems here is that, to simplify the example: $log_x(a) = x \implies x^x = a$ , which can only be solved numerically or by a really fortuitous value of a.

Frankly I don't deal with variable bases that often...I pretty much exclusively use the change of base formula to change it to a natural log.

-Dan