2 ^ x = 3^ Y = 6 ^Z
prove Z= X *Y / X + Z
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I think there is a mistake in this question here, we have to prove that Z = X*Y/X + Y
here, let
2^X = 3^Y = 6^Z = K
now
2 = K^1/X
3 = K^1/Y
6 = K^1/Z
now, we know that
2 x 3 = 6
K^1/X + K^1/Y = K^1/Z
K^(1/X+ 1/Y) = K^1/Z
now, comparing b/s we have,
1/X + 1/Y = 1/Z
X + Y/X*Y = 1/Z
Z = X*Y/X+Y
hence proved
HOPE THIS HELPS ^_^
here, let
2^X = 3^Y = 6^Z = K
now
2 = K^1/X
3 = K^1/Y
6 = K^1/Z
now, we know that
2 x 3 = 6
K^1/X + K^1/Y = K^1/Z
K^(1/X+ 1/Y) = K^1/Z
now, comparing b/s we have,
1/X + 1/Y = 1/Z
X + Y/X*Y = 1/Z
Z = X*Y/X+Y
hence proved
HOPE THIS HELPS ^_^
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