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Solve : root(4)(|x-3|^(x+1))=root(3)(|x-...

Solve : `root(4)(|x-3|^(x+1))=root(3)(|x-3|^(x-2))`.

Text Solution

Verified by Experts

The correct Answer is:
x = 4, 2 ; x = 11
`root(4)(|x-3|^(x+1))=root(3)(|x-3|^(x-2))`
Taking log on both the sides
`(x+1)/(4)log|x-3|=(x-2)/(3)log|x-3|`
`rArr log|x-3|[(x+1)/(4)-(x-2)/(3)]=0`
`rArr log|x-3|=0` or `[((x+1)/(4))-((x-2)/(3))]=0`
`rArr x=4, 2` or x = 11
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