What is the measurement of a Logarithmic

Bootsie

I was reading a book and it said the sun was 10^12 Logarithmic. What is the measurement of a Logarithmic?

DonAntonio

Put a link to that page in that book or try to quote it EXACTLY and/or read the definition. As far as I know, there's nothing like

"some number logarithmic" in general, though it could be that book's author's own definition of something.

DonAntonio

Bootsie

I cant quite get it but here it is, "The following scale of the universe is logarithmic, meaning that each division represents a 10-fold increase in size over the one before. The scale ranges over 40 orders of magnitude or increments of powers of 10." This is from the book, "Science Desk Reference"

phinds

Yes, that makes perfect sense (which your original post did not). Do you not understand logarithms / log scales?

Bootsie

I do not understand much of it only that it is the universal scale for very large or very small things.

DonAntonio

Oh, ok. So it seems to be the author uses a logarithmic scale to measure stuff. For example, using logarithms in

base 10, we can say that 1, 10, 100 are doubling logaritmic measures, and this means [tex]0=\log_{10}1\,,\,1=\log_{10}10\,,\,2=\log_{10}100[/tex] Thus, to say the sun is [itex]10^{12}[/itex] logarithmic probably means, for that author, that the sun is 12 times bigger than

something with pre-agreed measure unit of 1 (say, the Earth), since [itex]\log_{10}10^{12}=12\,\log_{10}10=12[/itex].

Of course, the sun is way bigger than 12 times the Earth.

DonAntonio

micromass

Maybe this is important: do you know what a logarithm is??

nucl34rgg

Logarithms don't normally have units.
Sometimes when you are dealing with really large numbers, it is better to express them on a log scale. One log scale you may be familiar with is the Richter scale for earthquakes.
For example, an 8.0 earthquake has a seismic wave amplitude 100, which is 10^2, times greater than that of a 6.0 earthquake.

EDIT: As said below, it would be more accurate to say "when dealing with a large range of differences between numbers, it is best to use the log scale."

phinds

No, that is not quite correct. Logarithms are used where a number RANGE is very large. If you want to make a plot that goes from 100,000,000 to 100,000,010 you would not very likely use logs. BUT if you want to make a plot that goes from 0 to 100,000,000 then you MIGHT use logs, depending on the distribution of the data. You should study up on logs / log scales.

HallsofIvy

Your original error, then, was grammatic. "Logarithmic" is not a noun, it is an adjective. In what you quote "logarithmic" modifies "scale". A logarithmic scale puts the data point (x, y) on the graph where, normally, (x, log(y)) would be. That is, the "y-axis" measures log(y), not y.

An advantage is that the (common) logarithm of [itex]10^n[/itex] is n and the logarithm of [itex]10^{-n}[/itex] is -n so that very large and very small amounts are changed to "workable" numbers.

Another is that graphs, (x, y), of exponential functions, such as [itex]y= c a^{bx}[/itex] become graphs of [itex]y= log(c a^{bx})= b log(a)x+ log(c)[/itex], a straight line with slope b log(a) and y-intercept log(c).

One disadvantage is that y must be positive.