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Solve: |x-1|^((log)(10)x)^2-(log)(10)x^2...

Solve: `|x-1|^((log)_(10)x)^2-(log)_(10)x^2=|x-1|^3`

Text Solution

Verified by Experts

We have
`|x-1|^((log_(10)x)^(2)-log_(10)x^(2))=|x-1|^(3)`.
`rArr x = 2 or (log_(10)x)^(2)-2log_(10)x-3=0`
` rArr x = 2 or (log_(10)x-3)(log_(10)x+1)=0`
` rArr x = 2 or log_(10)x = 3, log_(10) x =- 1`
` rArr x = 2, x= 1000 or x = 0.11`
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