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If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)...

If `x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,p rov et h a t1+x y z=2y zdot`

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`1+xyz=1(log_(2a)a)(log_(3a)2a)(log_(4a)3a)`
`=1+(loga)/(log2a)(log2a)/(log3a)(log3a)/(log4a)`
`=1+(loga)/(log4a)`
`=log_(4a)4a+log_(4a)a`
`=log_(4a)4a^(2)=2log_(4a)2a`
`=2(log_(3a)2a)(log_(4a)3a)=2yz`
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