Logarithmic vs exponential scales

[srfriggen]

can someone please explain the difference. Graphically and mathematically it is easy to see they are inverses. But I see certain scales like the Richter scale that seem to increase exponentially, but are labeled as logarithmic scales. for example, on the richter scale with each increase in magnitude there is an exponential increase in energy by a factor of 10 i believe. so the difference between a 5 and 6 magnitude earthquake is muuuuch greater than then energy of a 1 and 2 earthquake. seems to me that to graph this you would graph 10^x and have the magnitude on the x-axis and the energy on the y axis. but is the ricther scale and other logarithmic scales just the graph of log10x with the magnitude on the y-axis and energy on the x axis? seems it is just a matter of how you view it.

I know my question is vague, but I'm starting calc II in a week and a half and am trying to prepare as much as possible so any and all information regarding this topic would be very helpful.

Thank you.

 

[Char. Limit]

I think that graphs are split into logarithmic and linear...

 

[hotvette]

Richter scale is a base-10 log scale where the assigned value is the log of the measured magnitude.

http://en.wikipedia.org/wiki/Richter_magnitude_scale

Not sure what an exponential scale is. I've not heard of. I suppose you could plot e^y vs x on a graph, but can't think of a reason to do so. Plotting log₁₀y vs x or log_ey vs x is done all the time for convenience because a large range of y can be compactly represented.

 

[srfriggen]

I just meant something like y=10^x.

thanks for the info. I don't understand what the difference between "base 10" and "base -10". From what I read you would reflect the graph over the x-axis? Also, I thought you couldnt/shouldn't use a negative base for a logarithmic function?

 

[Char. Limit]

You can't...

It wouldn't be defined for positive numbers. For example, let's say I used... oh... $$log_{-2} 4=x$$. Rearranging, we get $$-2=4^x$$ which doesn't exist for any real, or perhaps any x.

 

[jacksonwalter]

You can't...

It wouldn't be defined for positive numbers. For example, let's say I used... oh... $$log_-2 4=x$$. Rearranging, we get $$-2=4^x$$ which doesn't exist for any real, or perhaps any x.

ehh...you can say $$e^{i\pi} = -1$$ and then say $$ln(-1) = i\pi$$ so that $$ln(-2) = ln(-1*2) = ln(-1) + ln(2) = i\pi + ln(2)$$ and get some complex values for x if you really wanted.

 

[Char. Limit]

That's why I had the perhaps in there. I knew it wasn't true that -2=4^x for a real x, but with complexes, who can tell?

Other than mathematicians, of course.