# Math Help - Why the log graphs are inversed?

1. ## 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.

2. 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.

3. 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

4. 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.

5. 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

6. 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 $y=x$.