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write the square root of 32as a power of 2 and hence solve the equation 16to the power of x-1=2 square root of 32

  • maths -

    since 32 = 2^5,

    sqrt(32) = 32^(1/2) = (2^5)^(1/2) = 2^(5/2)

    16^(x-1) = 2 * 2^(5/2) = 2^(1 + 5/2) = 2^(7/2)

    16 = 2^4

    2^(4x-4) = 2^(7/2)
    so,
    4x-4 = 7/2
    8x-8 = 7
    8x = 15
    x = 15/8

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