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2020-08-06
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Do logs have units?
The real deal is that you cannot take the log (or LN) of a number that actually has units, i.e., before the log (or LN) is applied, the unit must be dimensionless. You may be familiar with the concept of making quantities that otherwise have units, unitless, as being referred to as activities in chemistry.
Are logs Unitless?
Yes, logarithms always give dimensionless numbers, but no, it's not physical to take the logarithm of anything with units.
How does a logarithm affect units?
The units of a LN(p) would generally be referred to as “log Pa” or “log ATM.” Taking the logarithm doesn't actually change the dimension of the argument at all -- the logarithm of pressure is still pressure -- but it does change the numerical value, and thus “Pa” and “log Pa” should be considered different units.
What happens when you log a number?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
What happens to units in an exponential?
Almost always, a physical equation with an exponential function will have that function be dimensionless. (If it isn't dimensionless, it's probably because there is a constant of 1 with a unit secretly multiplied in.) All arguments to an exponential MUST be dimensionless.
What does a logarithmic scale show?
A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Rather, the numbers 10 and 100, and 100 and 1000 are equally spaced.
Why would you use a logarithmic scale?
There are two main reasons to use logarithmic scales in charts and graphs. The first is to respond to skewness towards large values. i.e., cases in which one or a few points are much larger than the bulk of the data. The second is to show percent change or multiplicative factors.
What is the difference between logarithmic and linear scale?
On a linear scale the value between any two points will never change. A logarithm is based on exponents, which are the superscripts next to, and above, another base number or variable. On a logarithmic scale the value between two points changes in a particular pattern.
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