Suppose that $q$ is a power $p^e$ of a prime number $p$. The calling sequence logp( q ) returns the exponent $e$. This is equivalent to log[p]( q ), except that the base $p$ of the logarithm is not generally known in advance.

if $q$ is a complex numeric that is not a power of a prime number then an exception is raised.

Otherwise, logp returns unevaluated.

Note that logp( 1 ) = 0.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$\mathrm{logp}\left(4\right)$

$2$

$\mathrm{logp}\left(2187\right)$

$7$

$\log \left[3\right]\left(2187\right)$

$7$

$\mathrm{logp}\left(181736602529563493772743207707225769267002557282133466635618621760664905776528650031297111433653361343413114922459355399125487176436206484922550339694292920308157658467185877862180743883366036055136650822122616340543983928298650053040147667730642467144039525033795872181721299778170114597245492905373163846425438075219742329773361475927592940713048575880678546342130536113739941714275612111016665973756986008654306628846785243192761535108469557914902031935282908398924790619171882023179658219569037894456670662283812638909841438734208283201\right)$

$40$

$\mathrm{logp}\left(12\right)$

Error, (in GroupTheory:-logp) argument is not a prime power

$\mathrm{logp}\left(1\right)$

$0$

$\mathrm{logp}\left({27}^{2f+4}\right)$

$6f+12$

$\mathrm{logp}\left(u+v\right)$

$\mathrm{logp}\left(u+v\right)$