SOLUTION: (2/5)^x = 25/4

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Question 187160: (2/5)^x = 25/4
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F5%29%5Ex+=+25%2F4

Since 25 can be written as 5%5E2
and 4 can be written as 2%5E2,
then 25%2F4 can be written as %285%2F2%29%5E2
Then we can flip the fraction inside the 
parentheses and change the sign of the exponent
and so altogether 25%2F4=%285%2F2%29%5E2=%282%2F5%29%5E%28-2%29.

So now we have

%282%2F5%29%5Ex+=+%282%2F5%29%5E%28-2%29

Now we can equate the exponents since the bases
are the same and positive and %22%22%3C%3E1

x=-2

Edwin