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Units[Standard]

 ln
 natural logarithmic function in the Standard Units environment
 log
 general logarithmic function in the Standard Units environment
 log10
 common logarithmic function in the Standard Units environment

Calling Sequence

 ln(expr) log(expr) log10(expr) log[b](expr) ${\mathrm{log}}_{b}\left(\mathrm{expr}\right)$

Parameters

 expr - algebraic expression b - algebraic expression, the base of the logarithm

Description

 • In the Standard Units environment, the arguments for the logarithmic functions can be unit-free, or multiplied by a unit that is energy-equivalent to a rational power of the dimension length(base)/length. Examples of such units are watt/watt(base) (power ratio) or voltage/voltage(base) (voltage ratio).
 • For non-unit-free expressions, the result is expressed in the dimension of logarithmic gain. The unit of the object returned is the neper by default.
 • For other properties, see the global function ln.

Examples

Notes:

 – To enter a unit in 2-D Math input, select the unit from the appropriate Units palette. If the unit you want is not there, select $\mathrm{unit}$ and then enter the unit.
 – When you edit a unit, double brackets appear around it.
 > $\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Standard}\right]\right):$
 > $\mathrm{VR}≔\mathrm{ln}\left(5.32\mathrm{Unit}\left(\frac{'\mathrm{volts}'}{'\mathrm{volts}\left(\mathrm{base}\right)'}\right)\right)$
 ${\mathrm{VR}}{≔}{1.671473303}{}⟦{\mathrm{Np}}⟧$ (1)
 > $\mathrm{PR}≔\mathrm{ln}\left(5.32\mathrm{Unit}\left(\frac{'\mathrm{watts}'}{'\mathrm{watts}\left(\mathrm{base}\right)'}\right)\right)$
 ${\mathrm{PR}}{≔}{0.8357366515}{}⟦{\mathrm{Np}}⟧$ (2)
 > $\mathrm{map}\left(\mathrm{convert},\left[\mathrm{VR},\mathrm{PR}\right],'\mathrm{units}','\mathrm{dB}'\right)$
 $\left[{14.51823264}{}⟦{\mathrm{dB}}⟧{,}{7.259116321}{}⟦{\mathrm{dB}}⟧\right]$ (3)
 > $\mathrm{convert}\left(\frac{'\mathrm{volts}'}{'\mathrm{volts}\left(\mathrm{base}\right)'},'\mathrm{dimensions}','\mathrm{energy}'\right)$
 $\frac{{\mathrm{length}}{}\left({\mathrm{base}}\right)}{{\mathrm{length}}}$ (4)
 > $\mathrm{convert}\left(\frac{'\mathrm{watts}'}{'\mathrm{watts}\left(\mathrm{base}\right)'},'\mathrm{dimensions}','\mathrm{energy}'\right)$
 $\frac{{{\mathrm{length}}{}\left({\mathrm{base}}\right)}^{{2}}}{{{\mathrm{length}}}^{{2}}}$ (5)

 See Also