# Why the log graphs are inversed?

• May 9th 2009, 03:17 AM
User Name
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.
• May 9th 2009, 03:36 AM
Plato
Quote:

Originally Posted by User Name
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.
• May 9th 2009, 03:46 AM
User 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 AM
HallsofIvy
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.
• May 9th 2009, 04:26 AM
User Name
Quote:

Originally Posted by HallsofIvy
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
• May 9th 2009, 04:30 AM
Plato
Quote:

Originally Posted by User Name
So how do we compare these 2 graphs?

The two graphs must ‘mirror images’ of each other where the mirror is $y=x$.