SOLUTION: if log(2 ,256)= x+y and log(3 ,81)= x-y, then what is the value of x and y

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Question 1010177: if log(2 ,256)= x+y and log(3 ,81)= x-y, then what is the value of x and y
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

log%282+%2C%28256%29%29=+x%2By
log%283+%2C%2881%29%29=+x-y
log%282+%2C%28256%29%29=+x%2By........256=2%5E8
log%282+%2C%282%5E8%29%29=+x%2By
8log%282+%2C%282%29%29=+x%2By....since log%282+%2C%282%29%29=1, we have
8%2A1=+x%2By
8=+x%2By........eq.1

log%283+%2C%2881%29%29=+x-y
log%283+%2C%283%5E4%29%29=+x-y
4log%283+%2C%283%29%29=+x-y
4%2A1=+x-y
4=+x-y.................eq.2

solve the system:
8=+x%2By........eq.1
4=+x-y.................eq.2
--------------------------------------add both eq.1 and eq.2
8%2B4=+x%2By%2Bx-y
12=+x%2Bcross%28y%29%2Bx-cross%28y%29
12=+2x
x=12%2F2
highlight%28x=6%29
go to 8=+x%2By........eq.1, substitute 6 for x and solve for y
8=+6%2By
8-6=y
highlight%28y=2%29