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Calculate : (i) log(2)root(4)(64root(3...

Calculate :
(i) `log_(2)root(4)(64root(3)(4^(-1)(8)^(-4/3)))`

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Explore conceptually related problems

Find the values : log_(3)root(4)((729)root(3)(9^(-1).(27)^(-4/3)))

Find the value of log_(1//3)root(4)(729*root(3)(9^(-1)*27^(-4//3))) .

Knowledge Check

  • root(3)(8 (sqrt3 -1)^(3))=

    A
    `sqrt3-1`
    B
    `8 (sqrt3 -1)`
    C
    `3 (sqrt3 -1)`
    D
    `2 (sqrt3 -1)`

  • log_(4)2^(-8) =

    A
    `-4`
    B
    `-3`
    C
    `-2`
    D
    `-1`

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    Solve : (i) log_(8)[log_(2){log_(3)(4^(x)+17)}] = 1/3

    int x^(3)root(3)(x^(4)-4)dx

    int((4x-3)dx)/(root(3)(4x^(2)-6x+9))

    Evaluate: int ((sqrtx)^3-root(3)(x))/(6root(4)(x))dx

    Consider equations x^(log_(y)x) = 2 and y^(log_(x)y) = 16 . The value of x is (a) 2^(root(3)2) (b) 2^(root(3)4) (c) 2^(root(3)64) (d) 2 root(3)256)

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