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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- May 9th 2009, 03:17 AMUser NameWhy 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. - May 9th 2009, 03:36 AMPlato
- May 9th 2009, 03:46 AMUser Name
Hi Plato, Sorry for my bad English (Doh).

here I drew them.

http://i42.tinypic.com/2ise175.gif

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 - May 9th 2009, 04:12 AMHallsofIvy
**Because**they are "inverse" functions just as your title implies.

If $\displaystyle y= 2^x$, then taking logarithm, base 2, of both sides, $\displaystyle log_2(y)= x$. Since the graph of a function is typically of y= f(x), your graph is of $\displaystyle y= log_2(x)$. The two graphs, of $\displaystyle y= 2^x$, which is the same as the graph of $\displaystyle x= log_2(y)$, and $\displaystyle y= log_2(x)$ 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. - May 9th 2009, 04:26 AMUser Name
- May 9th 2009, 04:30 AMPlato