Index Laws: Comparing 0.5^x & 2^x

[resurgance2001]

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

 

[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 $0.5 = \frac{1}{2} = 2^{-1}$.

 

[resurgance2001]

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]

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.

 

[resurgance2001]

Yes. That's definitely a valid analysis.

Thank you confirming that.