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What is the range of f(x) = log(x – 3)?

  • math -

    The range of any standard log function like yours is the set of real numbers.

    That is, choosing the appropriate value of x will yield any y value you want

    suppose we want y or f(x) to be -500
    -500 = log(x-3)
    x-3 = 10^-500
    x = 3 + 10^-500 , a number just a bit to the right of +3

    (the closer you get to +3 from the right, the larger into the negatives the y will become)

    try the same thing for large values of x
    e.g. x = 1 000 000 000
    y = log (1 000 000 000 - 3) = 8.999..

    to get really large values of y as an answer your x must be un-measurably large.

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