Sets of Logarithmic Equations
1. Solve the set of equations:
x + y = 34
log2x + log2y = 6 x,y >0 , x < 34
log2x + log2y = 6 x,y >0 , x < 34
Solution:
x + y = 34
log2x + log2y = 6 x,y >0 , x < 34
y = 34 -x
log2x + log2(34 – x) = 6
log2 ( x.(34 – x)) = log264
x.(34 –x) = 64
x2 – 34x + 64 = 0
(x- 32)( x-2) = 0
x1 = 32 v x2 = 2
y = 34 – x
y1 = 34 – 32 v y2 = 34 - 2
y1 = 2 v y2 = 32
K = {[32,2][2,32]}
x + y = 34
log2x + log2y = 6 x,y >0 , x < 34
y = 34 -x
log2x + log2(34 – x) = 6
log2 ( x.(34 – x)) = log264
x.(34 –x) = 64
x2 – 34x + 64 = 0
(x- 32)( x-2) = 0
x1 = 32 v x2 = 2
y = 34 – x
y1 = 34 – 32 v y2 = 34 - 2
y1 = 2 v y2 = 32
K = {[32,2][2,32]}
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