x y z
Given that
x
,
y
and
z
are positive real that are not 1, evaluate
x l o g ( z y ) × y l o g ( x z ) × z l o g ( y x ) .
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The answer is 1.
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2 solutions
use 1 0 b = x where b = l o g x
Similar method here. You will get 1 0 n where n = ( l g x ) ( l g y − l g z ) + ( l g y ) ( l g z − l g x ) + ( l g z ) ( l g x − l g y ) = 0 . It follows that 1 0 0 = 1 .
Let the expression be equal to a. take log on both sides. the exponents become coefficients. use log(n/m)=logn -logm and expand the whole of the expression. we see terms cancel out and finally we get log a =0 which means that a equals one