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Question
Find the value of x in the following:
`(13)^(sqrtx)=4^4-3^4-6`
Solution
Given `(13)^(sqrtx)=4^4-3^4-6`
`(13)^(sqrtx)=(2^2)^4-3^4-6`
`rArr(13)^(sqrtx)=2^8-3^4-6`
`rArr(13)^sqrtx=256-81-6`
`rArr(13)^sqrtx=169`
`rArr(13)^sqrtx=(13)^2`
On comparing we get,
`sqrtx=2`
On squaring both side we get,
x = 4
Hence, the value of x = 4.
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