SOLUTION: Solve the following simultaneous equation 1) log8(xy) = 3 2) log2(x) * log2(y) = 18

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Question 1069845: Solve the following simultaneous equation
1) log8(xy) = 3
2) log2(x) * log2(y) = 18
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%288%2C%28xy%29%29=3
xy=8%5E3
xy=512
.
.
.
log%282%2C%28x%29%29%2Alog%282%2C%28y%29%29=18
log%282%2C%28x%29%29%2Alog%282%2C%28512%2Fx%29%29=18
log%282%2C%28x%29%29%2A%28log%282%2C%28512%29%29-log%282%2C%28x%29%29%29=18
log%282%2C%28x%29%29%2A%289-log%282%2C%28x%29%29%29=18
Use a substitution,
u=log%282%2C%28x%29%29
u%289-u%29=18
-u%5E2%2B9u-18=0
u%5E2-9u%2B18=0
%28u-3%29%28u-6%29=0
Two "u" solutions,
u-3=0
u=3
and
u-6=0
u=6
So,
log%282%2C%28x%29%29=3
x=2%5E3
x=8
and
log%282%2C%28x%29%29=6
x=2%5E6
x=64
So
x=8,y=512%2F8=64
and
x=64,y=512%2F64=8