how does one solve an equation of the type a^x = b^x + c??

for the life of me i cant do it.

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- Oct 19th 2010, 04:14 AM #1

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- Oct 19th 2010, 06:44 AM #2

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- Oct 19th 2010, 06:45 AM #3

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- Oct 19th 2010, 06:48 AM #4

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- Oct 19th 2010, 06:50 AM #5

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- Oct 19th 2010, 07:00 AM #6

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- Oct 19th 2010, 07:04 AM #7
The logarithm of a sum is not something you can simplify. The identity only works the other way.

With this problem, I'd probably go for a numerical solution using Newton-Raphson. Of course, this assumes you know a, b, and c, and that a and b are both positive. Is that the case?

- Oct 19th 2010, 07:58 AM #8

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- Oct 19th 2010, 08:01 AM #9

- Oct 19th 2010, 08:08 AM #10

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- Oct 19th 2010, 08:11 AM #11
Right, but you can always convert an equation-solving problem into a root-finding problem by throwing everything on to one side of the equation thus:

$\displaystyle f(x)=a^{x}-b^{x}-c=0.$

Then you use Newton-Raphson on $\displaystyle f(x).$

If you have convergence problems, and your solutions are oscillating wildly, then you probably don't have a solution for that particular combination of a, b, and c. That's a little warning sign you can look for.