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Math Help - ln(x) and e^x

  1. #1
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    ln(x) and e^x

    Recall that y = ln(x) and y = e^x are inverse functions. THe graph of y = ln(x) looks as though it might be approaching a horizontal asymptote. Write an argument based on the graph of y = e^x to explain why it does not.
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  2. #2
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    Think Domain of of y = e^x and Range of y = ln(x).
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  3. #3
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    does this make sense:


    Since they are inverse functions, every (x,y) pair of ln(x) corresponds to a pair (y,x) of e^x. If ln(x) approaches a horizontal asymptote, that means that y has a limit. That means there is a limit on the x values of f(x). This is ridiculous, so obviously there is no horizontal asymptote for ln(x).
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  4. #4
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    It's a little colloquial, rather than technical, but I like it.
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  5. #5
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    how would you explain it technically?
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  6. #6
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    Fewer words and more symbols.
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