Question

Can someone tell me the logarithmic equation that matches up to this graph? Please do not just give the answer, I would like to learn how to do this for future problems as well.

Answer 1

That graph looks like an exponential, not a log? Logs have a vertical asymptote, not a horizontal. Do you have answer choices?

Answer 2

Assuming that it is an exponential, the fact that it's decreasing tells you something about the base. Do you know what that means?

Answer 3

\[(1/4)^{x+2}\]
\[(1/4)^x+2\]
\[(1/4)^{x-2}\]
\[(1/4)^x-2\]

Answer 4

It is an exponential equation, not logarithmic, sorry

Answer 5

SOMEONE HELP PLEASE!

Answer 6

\[(1/4)^x+2\\4^{-x}+2\]

above is the first option, i have just re-arranged it a bit. do you understand what i did with it?

Answer 7

*above is the SECOND option

Answer 8

yes i understand

Answer 9

as x increases \(4^{-x}\) keeps getting smaller and smaller.

in other words, if x tends to infinity, \(4^{-x}\) tends to zero.

so that means \(4^{-x}+2\) should get closer and closer to 2 as x increases.

makes sense?

Answer 10

yes

Answer 11

Thats not the case, it gets closer and closer to y=0

Answer 12

so that ones not it

Answer 13

yes!

you can make the same argument for option 4. except it will get closer to (-2)

Answer 14

Yes. So if the translation is to the left, then I need +2 inside the exponent right?

Answer 15

perfect :)

Answer 16

So the answer would be A?

Answer 17

yes.its A

Answer 18

Thanks!