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If 3^x=5^y=(75)^z show that z=(xy)/(2x+y...

If `3^x=5^y=(75)^z` show that `z=(xy)/(2x+y`

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let `3^x=5^y=75^z=k`
`3=k^(1/x)`,`5=k^(1/y)`,`75=k^(1/z)`
now `5^2xx3=k^(1/z)`
`(k^(1/y))^2xxk^(1/x)=k^(1/z)`
we have `2/y+1/x=1/z`
or, `z=(xy)/(2x+y)`
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