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0:14 2:02 Suggested clip Condensing a logarithmic expression into one single quantity using YouTubeStart of suggested client of suggested clip Condensing a logarithmic expression into one single quantity using
0:07 4:01 Suggested clip Express As Single Logarithms Example — 3 / Logarithms — Math YouTubeStart of suggested client of suggested clip Express As Single Logarithms Example — 3 / Logarithms — Math
0:27 7:00 Suggested clip 101 Write a Logarithmic Expression as a Single Logarithm (4.4 YouTubeStart of suggested client of suggested clip 101 Write a Logarithmic Expression as a Single Logarithm (4.4
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.
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.
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.
Yes, logarithms always give dimensionless numbers, but no, it's not physical to take the logarithm of anything with units.
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.

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