In the Natural Units environment, the arguments for the exponential functions can be unit-free, or multiplied by a unit with the dimension logarithmic_gain. An error is returned if the dimension of the argument is not one of logarithmic gain.

By default, the units of the object returned are a ratio of wave numbers (inverse length). Using energy conversions, this ratio is proportional to a voltage ratio and its square is proportional to a power ratio.

Note that the first calling sequence must be entered in 2-D math notation by using either the palettes or command completion. The exponential $e^x$ will not be recognized if it is entered manually.

For other properties, see the global function exp.

$\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Natural}\right]\right)\:$

$\mathrm{ratio}≔\exp \left(15.5\mathrm{dB}\right)$

$\mathrm{ratio}≔5.956621435⟦\frac{m\left(\mathrm{base}\right)}{m}⟧$

$\mathrm{convert}\left(\mathrm{ratio}\,'\mathrm{units}'\,\frac{\mathrm{volts}}{\mathrm{volts}\left(\mathrm{base}\right)}\,'\mathrm{energy}'\right)$

$5.956621435⟦\frac{V}{V\left(\mathrm{base}\right)}⟧$

$\mathrm{convert}\left({\mathrm{ratio}}^2\,'\mathrm{units}'\,\frac{\mathrm{watt}}{\mathrm{watt}\left(\mathrm{base}\right)}\,'\mathrm{energy}'\right)$

$35.48133892⟦\frac{W}{W\left(\mathrm{base}\right)}⟧$

$\mathrm{log10}\left(\right)$

$0.7750000000⟦\mathrm{Np}⟧$

$\mathrm{convert}\left(\,'\mathrm{units}'\,\mathrm{dB}\right)$

$6.731564469⟦\mathrm{dB}⟧$

$\ln \left(\right)$

$1.784503447⟦\mathrm{Np}⟧$

$\mathrm{convert}\left(\,'\mathrm{units}'\,\mathrm{dB}\right)$

$15.50000000⟦\mathrm{dB}⟧$

$\ln \left(\exp \left(15.5\mathrm{dB}\right)\right)$

$1.784503447⟦\mathrm{Np}⟧$