SOLUTION: Help me with this simultaneous equations {{{2^x-5^y=3}}} and {{{2^(x-2)+5^(y-2)=2}}}

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Question 1072984: Help me with this simultaneous equations
2%5Ex-5%5Ey=3
and
2%5E%28x-2%29%2B5%5E%28y-2%29=2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Ex-5%5Ey=3 --> 4%2A2%5E%28x-2%29+-+25%2A5%5E%28y-2%29+=+3
and
2%5E%28x-2%29%2B5%5E%28y-2%29=2
------------
4%2A2%5E%28x-2%29+-+25%2A5%5E%28y-2%29+=+3
2%5E%28x-2%29%2B5%5E%28y-2%29=2
--------
Sub r for 2^(x-2) and s for 5^(y-2)
4r - 25s = 3
2r + s = 2 times 2 --> 4r + 2s = 4
-----------
4r - 25s = 3
4r + 2s = 4
----------------------- Subtract
-27s = -1
s = 1/27
r = 53/54
================
2%5E%28x-2%29+=+r+=+53%2F54
(x-2)*log(2) = log(53/54)
x = 2 + log(53/54)/log(2)
----------
Solve for y the same way.