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Question
If \[\frac{x}{x^{1 . 5}} = 8 x^{- 1}\] and x > 0, then x =
Options
\[\frac{\sqrt{2}}{4}\]
\[\sqrt[2]{2}\]
4
64
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Solution
For `x /(x^1.5) = 8x^-1`, we have to find the value of x.
So,
`x^1 /(x^1.5) = 8x^-1`
`x ^(1-1.5) = 8x^-1`
`x ^(-0.5) = 2^3x^-1`
`(x^0.5) /x^-1= 2^3`
`x^(-5/10) /x^-1= 2^3`
`x^(-1/2+1)= 2^3`
`x^(-1/2+2/2)= 2^3`
`x^((-1+2)/2) = 2^3`
`x^(1/2) = 2^3`
By raising both sides to the power 2 we get
`x^(1/2xx2) = 2 ^(3xx2)`
`x^(1/2xx2) = 2 ^6`
`x^1 = 64`
The value of x is 64.
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