MATH

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Suppose 81^x = 64. What is 27^{x+1}?

Give me a clear explanation with the answer. Thanks! :)

  • MATH -

    clearly, x = log8164 = 1/4 log364

    27^{x+1} = 27*3^3x
    = 27*3^(3(1/4 log364))
    = 27*3^(3/4 log364)
    = 27*3^((log364) * 3/4)
    = 27*64^(3/4)
    = 27*2^(9/2)
    = 27*16√2
    = 432√2

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