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1.

`log(x-y)-log5-1/2logx-1/2logy=0` then find the value of `y/x+x/y=?`

Answer» `log(x-y) - log5 -1/2logx - 1/2logy = 0`
`=>log(x-y) - log5 -1/2(logx + logy) = 0`
`=>log(x-y) - log5 -1/2(logxy) = 0`
`=>2log(x-y) - 2log5 -(logxy) = 0`
`=>log(x-y)^2 - log5^2 -(logxy) = 0`
`=>log(x-y)^2 -(logxy) = log5^2`
`=>log((x-y)^2/(xy)) = log25`
`=>(x-y)^2/(xy) = 25`
`=>x^2+y^2-2xy = 25xy`
`=>x^2+y^2 = 27xy`
Dividing both sides by `xy`,
`=>x/y +y/x = 27`
Discussion
2.

Find domain of the function ` log_10 log_10 log_10 log_10 log_10 x`

Answer» `log_10log_10log_10log_10 x>0`
`log_10log_10log_10 x>10^0`
`log_10^xlog_10^x>10^1`
`log_10^xlog_10^x>10`
`log_10^x>10^10`
`x>10^(10^10)`.
Discussion