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if 4^x - 4^x-1 = 24, then find value of x. please explain.

  • math -

    4 ^ ( x - 1 ) = 4 ^ x / 4 ^ 1 = 4 ^ x / 4


    4 ^ x - 4 ^ ( x - 1 ) = 24

    4 ^ x - 4 ^ x / 4 = 24

    4 * 4 ^ x / 4 - 4 ^ x / 4 = 24

    3 * 4 ^ x / 4 = 24 Multiply both sides by 4

    3 * 4 ^ x = 96 Divide both sides by 3

    4 ^ x = 32

    x * log ( 4 ) = log ( 32 ) Divide both sides by log ( 4 )

    x = log ( 32 ) / log ( 4 )

    x = 3.465736 / 1.386294

    x = 2.5

    x = 5 / 2


    log is " Natural logarithm " ( Logarithm with base e )

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