Logarithm Laws Cheat Sheet

By Dr. Iris Vaughan, Mathematics Editor·Published 1 October 2025·Last reviewed 10 January 2026

All logarithm identities — product, quotient, power, change of base — with the natural log and common log versions, and worked examples.

Key Formulas

log(xy)=logx+logy
log(x/y)=logx−logy
log(xⁿ)=nlogx
Change of base: logₐx=logx/loga
ln(eˣ)=x
e^(lnx)=x
log 1=0
log base=1

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