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=== Kebalikan dari fungsi eksponensial lainnya ===
Eksponensiasi muncul dalam cabang matematika dan fungsi inversnya seringkali mengacu pada logaritma. Sebagai contoh, [[logaritma matriks]] merupakan fungsi invers (bernilai banyak) dari [[eksponensial matriks]].<ref>{{Citation|last1=Higham|first1=Nicholas|author1-link=Nicholas Higham|title=Functions of Matrices. Theory and Computation|location=Philadelphia, PA|publisher=[[Society for Industrial and Applied Mathematics|SIAM]]|isbn=978-0-89871-646-7|year=2008}}, chapter 11.</ref> Contohnya lain seperti [[Fungsi logaritma p-adik|fungsi logaritma ''p''-adik logarithm]], fungsi invers dari [[fungsi eksponensial p-adik|fungsi eksponensial ''p''-adik]]. Kedua fungsi tersebut didefinisikan melalui deret Taylor yang analog dengan kasus bilangan real.<ref>{{Neukirch ANT|mode=cs2}}, section II.5.</ref> Dalam konteks [[geometri diferensial]], [[Peta eksponensial (geometri Riemann)|peta eksponensial]] memetakan [[ruang garis singgung]] di sebuah titik [[Manifold terdiferensialkan|manifold]] ke [[Tetangga (matematika)|tetangga]] titik tersebutof that pointtersebut. Its inverse is also called theKebalikannya logarithmicjuga (ordisebut log)peta maplogaritma.<ref>{{Citation|last1=Hancock|first1=Edwin R.|last2=Martin|first2=Ralph R.|last3=Sabin|first3=Malcolm A.|title=Mathematics of Surfaces XIII: 13th IMA International Conference York, UK, September 7–9, 2009 Proceedings|url=https://books.google.com/books?id=0cqCy9x7V_QC&pg=PA379|publisher=Springer|year=2009|page=379|isbn=978-3-642-03595-1}}</ref>
 
InDalam the context ofkonteks [[finitegrup groupshingga]], exponentiationeksponensiasi isdinyatakan givendengan bymengalikan repeatedlysatu multiplyinganggota onegrup group element&nbsp;{{mvar|b}} withdengan itself.dirinya Thesecara berulang. [[discreteLogaritma logarithmdiskret]] ismerupakan thebilangan integerbulat&nbsp;''{{mvar|n}}'' solvingyang themenyelesaikan equationpersamaan
 
: <math>b^n = x,</math>
 
wheredengan {{mvar|x}} isadalah ananggota elementdari of the groupgrup. CarryingMengerjakan outsolusi theeksponensiasi exponentiationdapat candilakukan bedengan done efficientlyefisien, but the discrete logarithmnamun islogaritma believeddiskret todipercayai bebahwa verysangat hardsulit tountuk calculatemenghitungnya indalam somebeberapa groupsgrup. This asymmetry has important applications in [[public key cryptography]], such as for example in the [[Diffie–Hellman key exchange]], a routine that allows secure exchanges of [[Cryptography|cryptographic]] keys over unsecured information channels.<ref>{{Citation|last1=Stinson|first1=Douglas Robert|title=Cryptography: Theory and Practice|publisher=[[CRC Press]]|location=London|edition=3rd|isbn=978-1-58488-508-5|year=2006}}</ref> [[Zech's logarithm]] is related to the discrete logarithm in the multiplicative group of non-zero elements of a [[finite field]].<ref>{{Citation|last1=Lidl|first1=Rudolf|last2=Niederreiter|first2=Harald|author2-link=Harald Niederreiter|title=Finite fields|publisher=Cambridge University Press|isbn=978-0-521-39231-0|year=1997|url-access=registration|url=https://archive.org/details/finitefields0000lidl_a8r3}}</ref>
 
{{anchor|double logarithm}}Further logarithm-like inverse functions include the ''double logarithm''&nbsp;{{math|ln(ln(''x''))}}, the ''[[Super-logarithm|super- or hyper-4-logarithm]]'' (a slight variation of which is called [[iterated logarithm]] in computer science), the [[Lambert W function]], and the [[logit]]. They are the inverse functions of the [[double exponential function]], [[tetration]], of {{math|''f''(''w'') {{=}} ''we<sup>w</sup>''}},<ref>{{Citation|last1=Corless|year=1996|archive-date=14 December 2010|archive-url=https://web.archive.org/web/20101214110615/http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf|access-date=13 February 2011|s2cid=29028411|doi=10.1007/BF02124750|pages=329–59|volume=5|issn=1019-7168|journal=Advances in Computational Mathematics|url=http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf|first1=R.|title=On the Lambert ''W'' function|author5-link=Donald Knuth|first5=Donald|last5=Knuth|first4=D.|last4=Jeffrey|first3=D.|last3=Hare|first2=G.|last2=Gonnet|url-status=dead}}</ref> and of the [[logistic function]], respectively.<ref>{{Citation|last1=Cherkassky|first1=Vladimir|last2=Cherkassky|first2=Vladimir S.|last3=Mulier|first3=Filip|title=Learning from data: concepts, theory, and methods|publisher=[[John Wiley & Sons]]|location=New York|series=Wiley series on adaptive and learning systems for signal processing, communications, and control|isbn=978-0-471-68182-3|year=2007}}, p.&nbsp;357</ref>
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