SOLUTION: (-9x + 57)^x = 729, find x.

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Question 1210272: (-9x + 57)^x = 729,
find x.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28-9x+%2B+57%29%5Ex+=+729

When the unknown in an equation appears as an exponent as well as a term or
factor, there is no way to solve it but by trial and error or some iterative
method which amounts to trial and error.

Since 729 = 36, you might try 6:

%28-9%286%29+%2B+57%29%5E6+=+729=3%5E6

%28-54%2B57%29%5E6+=+3%5E6

%28-3%29%5E6+=+3%5E6

So 6 is a solution.

With a graphing calculator, you can also get another solution, although
this one is approximate:

x = 1.7746996


       graph%28350%2C10%2C0%2C7%2C-400%2C3%29


Edwin