SOLUTION: Please help me in solving this question. - Find the value of : - {{{(log base 3 (4)+ log base 2 (9))^2 - (log base 3 (4)- log base 2 (9))^2}}}

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Question 137921: Please help me in solving this question. - Find the value of : -
%28log+base+3+%284%29%2B+log+base+2+%289%29%29%5E2+-+%28log+base+3+%284%29-+log+base+2+%289%29%29%5E2
Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
(log base 3 (4)+ log base 2 (9))^2 - (log base 3 (4)- log base 2 (9))^2
Let log3 4 = x and log2 9 = y
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You have:
(x+y)^2 -(x-y)^2
= x^2+2xy+y^2-(x^2-2xy+y^2)
= 4xy
---------
Substituting bac to logs you get:
= 4(log3 4)(log2 9)
= 4[log4/log3][log9/log2]
= 4[log4/log2][log9/log3]
= 4 [log2 4][log3 9]
= 4 [2][2]
= 16
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Cheers,
Stan H.
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