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Question
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
Solution
Let 3x = 5y = (75)z = k
`rArr3=k^(1/x),` `5=k^(1/y),` `75=k^(1/z)`
`rArr5^2xx3=k^(1/z)`
`rArr(k^(1/y))^2xxk^(1/x)=k^(1/z)`
`rArrk^(2/y)xxk^(1/x)=k^(1/z)`
`rArrk^(2/y+1/x)=k^(1/z)`
`rArr2/y+1/x=1/z`
`rArr(2x+y)/(xy)=1/z`
`rArrz=(xy)/(2x+y)`
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