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Math Help - Why the log graphs are inversed?

  1. #1
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    Exclamation Why the log graphs are inversed?

    Hi, just wondering...
    for example Y=log2^x why does it lies on 1 in x axis and not Y axis like the graph of Y=2^x?

    Thanks.
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  2. #2
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    Quote Originally Posted by User Name View Post
    for example Y=log2^x why does it lies on 1 in x axis and not Y axis like the graph of Y=2^x?
    What does that mean?
    Please, write it more clearly so we might understand what you are trying to ask.
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  3. #3
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    Hi Plato, Sorry for my bad English .
    here I drew them.

    as you can see the graph, black line is the graph of log, my question is why does it inverse? and the red one is the graph of Y=2^x.
    we know that any base with exponent zero gives 1 right? but why the '1' on black one(log one) is on X axis and on the other one is on Y axis?
    Thanks
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  4. #4
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    Because they are "inverse" functions just as your title implies.

    If y= 2^x, then taking logarithm, base 2, of both sides, log_2(y)= x. Since the graph of a function is typically of y= f(x), your graph is of y= log_2(x). The two graphs, of y= 2^x, which is the same as the graph of x= log_2(y), and y= log_2(x) just have x and y reversed: (0, 1) on one graph becomes (1, 0) on the other.

    This is a general property of graphs of "inverse" functions: The point (a, b) on one corresponds to (b, a) on the other.
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  5. #5
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    Quote Originally Posted by HallsofIvy View Post
    Because they are "inverse" functions just as your title implies.

    If y= 2^x, then taking logarithm, base 2, of both sides, log_2(y)= x. Since the graph of a function is typically of y= f(x), your graph is of y= log_2(x). The two graphs, of y= 2^x, which is the same as the graph of x= log_2(y), and y= log_2(x) just have x and y reversed: (0, 1) on one graph becomes (1, 0) on the other.

    This is a general property of graphs of "inverse" functions: The point (a, b) on one corresponds to (b, a) on the other.
    So how do we compare these 2 graphs?

    Ta
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  6. #6
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    Quote Originally Posted by User Name View Post
    So how do we compare these 2 graphs?
    The two graphs must ‘mirror images’ of each other where the mirror is y=x.
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