Solving for "X"-ponents

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
GreenLantern
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Solving for "X"-ponents

Postby GreenLantern » Wed Feb 02, 2011 4:59 pm

I have a relatively simple equation, but am not sure I'm going about it in the right way.



My assumption is that I need to get the bases equal. The only way I know how to do this is to raise them to equalizing powers, the only number that can do that is 0. (This is the part I'm unsure of.)



After that the problem is really simple. The bases can be nixed and equations solved.




But that makes no sense... Plugging that in gets an obviously wrong answer, so I return to the part I'm unsure of and am now here. :mrgreen:

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stapel_eliz
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Postby stapel_eliz » Wed Feb 02, 2011 6:41 pm

GreenLantern wrote:

My assumption is that I need to get the bases equal.

Since 9 is not a whole-number or fractional power of 2, no, trying to get equal bases (so you can equate the powers) isn't going to work. You're stuck with logarithms:

. . . . .

. . . . .

Divide through by , subtract the , and then divide through by the to get an expression for .

Don't simplify (that is, plug it into your calculator to find a decimal approximation) unless instructed to do so. :wink:


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