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If ( log 6)/(log 12) =xand (log 54)/log 24=yFindxy+ 5x-2y+4

sahil suman , 7 Years ago
Grade 12th pass
anser 1 Answers
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Last Activity: 7 Years ago

Let a       =log23
x = \frac{1+a}{2+a}
y=\frac{1+3a}{3+a}
Replace in equaton
xy+5x-2y+4
= \frac{(1+a)(1+3a)}{(2+a)(3+a)}+5.\frac{1+a}{2+a}-2.\frac{1+3a}{3+a}+4
=\frac{(1+3a)(1+a-2(2+a))+5(3+a)(1+a)}{(2+a)(3+a)}
=\frac{(-3-a)(1+3a)+5(3+a)(1+a)}{(2+a)(3+a)} + 4
=\frac{(-3-a)(1+3a)+5(3+a)(1+a)}{(2+a)(3+a)} + 4
= \frac{(a+3)(-1-3a+5(1+a))}{(2+a)(3+a)} + 4 
 
= \frac{(4+2a)(a+3)}{(2+a)(3+a)} + 4 =2+4 = 6

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