How is
Y=2^x
geometrically transformed into
3^5x/2

Question

anonymous · Answer

Is that $$y=2^x, y=3^{\frac{5x}{2}}$$?

anonymous · Answer

Yes, it is

anonymous · Answer

I thought it was a stretch in the x-axis by 2.5, 
Apparently, it's by 0.4??

anonymous · Answer

Ohhh I made a mistake..! It's supposed to be$$ Y=3^x$$

anonymous · Answer

and another one like that is the transformation of $$y=3^x$$ onto $$y=9^x$$

Again, I got a stretch in the x-axis by S.F. 3, but it's by S.F 0.5

anonymous · Answer

let look at $$y=ab^{cx}$$
okay it seems that to find the stretch in the x axis it will be $$\frac{1}{c}$$
I think that solves the problem. 

I'll keep looking to find a site that can show this with a general form.

anonymous · Answer

For the second example you wrote the equations will be 
$$y=3^x, y=9^x=3^{2x}$$
So the stretch is 1/2 or 0.5

anonymous · Answer

I see what you mean, but I'm not sure why that's the formula lol...

anonymous · Answer

This site explains it well the only thing is that it looks at e^x graphs which aren't any different from your ones. http://archives.math.utk.edu/visual.calculus/0/shifting.5/index.html

anonymous · Answer

Oh, Ok. Thanks :)

anonymous · Answer

If you type both equations into Wolfram Alpha you can see it visually as well. For y=3^x from -2 to 2 is shown exactly the same as y=9^x but only for -1 to 1. So half the space. 

I'm still not sure on the formula though, sorry.