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Math Help - Finding range of ln equation. Without calculator

  1. #1
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    Finding range of ln equation. Without calculator

    i know the domain is (-3 , infinity)

    y = ln(x+3)

    i thought it was [-4, infinity) but i checked on a calculator and it goes passed -4. And i cannot use a calculator
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  2. #2
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    The range of a function is the set of numbers the function can achieve. The natural log has a range (-\infty,\infty). However, its domain is (-3,\infty). The domain is the set of numbers for which the function is defined. Natural log can take numbers from (0,\infty). So we just need to check when x+3 > 0.
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  3. #3
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    What is the range of \ln x ?
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  4. #4
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    An easy way to remember the range of the natural log is to recall that  ln|a| = x \implies   a = e^x .
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  5. #5
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    its (-inf, inf) so all real numbers?
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  6. #6
    Senior Member eumyang's Avatar
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    Yep!

    It may be helpful to remember from now on that the domain of the basic f(x) = ln x is (0, ∞) and that the range is (-∞, ∞). In my textbook it's considered one of the twelve basic functions.
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