# Index laws question

## Homework Statement

we are asked to compare the graphs of 0.5^x with 2^x using index laws

## Homework Equations

I am not sure how the regular index laws apply

## The Attempt at a Solution

All I can say at the moment is the the graph of 2^x is a reflection of 0.5^x in the Y axis. I don't know how exactly to compare or justify this using index laws

## Answers and Replies

Related Precalculus Mathematics Homework Help News on Phys.org
S.G. Janssens
By "index laws", do you mean the rules for manipulation of quantities involving bases and exponents?

It may help to note that $0.5 = \frac{1}{2} = 2^{-1}$.

So then 0.5^x becomes 2^-x? So the two functions are effectively 2^x and 2^-x and because of this they are reflections of each other in the Y - axis.

I don't know what else the teacher might be expecting but I suspect that the answer the teacher is looking for. What do you reckon? The question was a bit vague.

Thanks

S.G. Janssens
What do you reckon?
I think you are correct.

SammyS
Staff Emeritus
Homework Helper
Gold Member
So then 0.5^x becomes 2^-x? So the two functions are effectively 2^x and 2^-x and because of this they are reflections of each other in the Y - axis.

Thanks
Yes. That's definitely a valid analysis.

Yes. That's definitely a valid analysis.

Thank you confirming that.