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Units[Natural]

 ln
 natural logarithmic function in the Natural Units environment
 log
 general logarithmic function in the Natural Units environment
 log10
 common logarithmic function in the Natural 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 Natural 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).
 • By default, the unit of the object returned is the nepers.
 • For other properties, see the global function ln.

Examples

 > $\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Natural}\right]\right):$
 > $\mathrm{VR}≔\mathrm{ln}\left(\frac{5.32\mathrm{volts}}{\mathrm{volts}\left(\mathrm{base}\right)}\right)$
 ${\mathrm{VR}}{≔}{1.671473303}{}⟦{\mathrm{Np}}⟧$ (1)
 > $\mathrm{PR}≔\mathrm{ln}\left(\frac{5.32\mathrm{watts}}{\mathrm{watts}\left(\mathrm{base}\right)}\right)$
 ${\mathrm{PR}}{≔}{0.8357366515}{}⟦{\mathrm{Np}}⟧$ (2)
 > $\mathrm{dbls}≔\mathrm{map}\left(\mathrm{convert},\left[\mathrm{VR},\mathrm{PR}\right],'\mathrm{units}',\mathrm{dB}\right)$
 ${\mathrm{dbls}}{≔}\left[{14.51823264}{}⟦{\mathrm{dB}}⟧{,}{7.259116321}{}⟦{\mathrm{dB}}⟧\right]$ (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)
 > $\mathrm{map}\left(\mathrm{exp},\mathrm{dbls}\right)$
 $\left[{5.319999998}{}⟦\frac{{m}{}\left({\mathrm{base}}\right)}{{m}}⟧{,}{2.306512518}{}⟦\frac{{m}{}\left({\mathrm{base}}\right)}{{m}}⟧\right]$ (6)