A logarithmic unit is a unit that can be used to express a quantity (physical or mathematical) on a logarithmic scale, that is, as being proportional to the value of a logarithm function applied to the ratio of the quantity and a reference quantity of the same type. The choice of unit generally indicates the type of quantity and the base of the ...

2012年11月16日 · Overall, the argument $x$ of $\ln(x)$ must be unitless, and a log transformed quantity must be unitless. If $x = 0.5$ is measured in some units, say, seconds, then taking the log actually means $\ln(0.5s/1s) = \ln(0.5)$. See this for more information about other transcendental functions. Hope this helps.

可以使用编程语言中的数学库计算对数。例如，在Python中，可以使用 `math.log` 函数计算自然对数和其他底数的对数：

2007年3月20日 · 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.

When you take the log of a product, you get the sum of the logs, so log(1 km) is the same as log(1)+log(km). This shows that the log of 1 km is neither a dimensionless quantity nor a dimensionful one.

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2020年11月7日 · What happens to units when we take the Ln of the both side of the equation? For example for an equation $PV^k = C$ (which becomes $\ln P = -k \ln V + \ln C$), how can we find the units of $k$ and $...

In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes.

The simple fact is that no function needs its definition extended to cope with units, because the standard functions used throughout maths and physics—which all act on dimensionless numbers and return a dimensionless number—are always sufficient for …

2022年1月22日 · You could show the actual numbers (e.g., $10^3$, $10^4$) and label the axis as “time [s]”, or you could plot the logarithms (e.g., 3, 4) and label the axis as “ $\log_{10} \frac{\mathrm{time}}{1\ \mathrm{s}}$ [unitless]”. Some people will abbreviate this as “log(time) []” and figure they’ll be understood.