help! How would I graph this using a graphing calculator?

$ 7^x3^x$

Question

help! How would I graph this using a graphing calculator?

$ 7^x>3^x$

bloomlocke367 · Answer

@IrishBoy123

solomonzelman · Answer

this equation just contains the x, and therefore I am really suspicious that this is not the initial question

solomonzelman · Answer

Or is it still the initial question -  to graph $7^x>3^x$ ?

bloomlocke367 · Answer

it is tho.. I can pull up the review packet online and screenshot it.

bloomlocke367 · Answer

http://prntscr.com/9mkb6k

solomonzelman · Answer

oh that is a little different

solomonzelman · Answer

to "solve the system graphically.

solomonzelman · Answer

so you are, I think, graphing two functions

$\color{#000000 }{ \displaystyle f(x)=7^x  }$
$\color{#000000 }{ \displaystyle g(x)=3^x  }$

(I am labelling them f(x) and g(x) for convinience)

And you want to know for which values of x is $\color{#000000 }{ \displaystyle 7^x>3^x  }$

solomonzelman · Answer

Well, I mean to say:

you want to know for which values of x is $\color{#000000 }{ \displaystyle f(x)>g(x) }$,

but this is really the same thing

solomonzelman · Answer

((Although there is a much easier way to tell without graphing))

bloomlocke367 · Answer

so.. I graph them separately?

bloomlocke367 · Answer

@SolomonZelman, sorry I had to do something for my dad.

solomonzelman · Answer

yes, graph them separately, and tell me where f(x)>g(x)

bloomlocke367 · Answer

oki. One second

bloomlocke367 · Answer

I'm not sure what I'm looking for tbh .-.

bloomlocke367 · Answer

wait. I see now XD

bloomlocke367 · Answer

when x is greater than 0. I had to zoom in on my calculator

bloomlocke367 · Answer

Thanks for helping :D

solomonzelman · Answer

YW

anonymous · Answer

$$7^x>3^x~only~if~x>0$$

solomonzelman · Answer

You can also tell this not graphically:

let $c$ be any positive number (even really really close to 0):
$\color{#000000 }{ \displaystyle 7^c>3^c  }$

$\color{#000000 }{ \displaystyle 7^0=3^0  }$


$\color{#000000 }{ \displaystyle 7^{-c}~~~~~?~~~~~3^{-c}  }$

$\color{#000000 }{ \displaystyle \frac{1}{7^c}~~~~~?~~~~~\frac{1}{3^c}  }$

$\color{#000000 }{ \displaystyle \frac{1}{7^c}~~~~~<~~~~~\frac{1}{3^c}  }$

(you are dividing by larger value on the right, therefore the result is smaller)

solomonzelman · Answer

by -c, I am denoting a negative number.
(Since c is a positive number)

solomonzelman · Answer

Oh m,y bad, you are dividing by a larger value on the left (not right)

solomonzelman · Answer

confused my left and rght :D

bloomlocke367 · Answer

haha, it's okay. thanks!

solomonzelman · Answer

yw