Home/Algebra/Exponentials and logarithms/Definition of logarithm12. Exponentials and logarithmsDefinition of logarithmLevel: fundamentalIn 12. Exponentials and logarithmsFormulaCopy LaTeXlogbx=y ⟺ by=x\log_bx=y\iff b^y=xlogbx=y⟺by=xEquivalent formCopy LaTeXb>0,b≠1,x>0b>0,\quad b\ne1,\quad x>0b>0,b=1,x>0Tagsalgebraexponentials logarithmsalgebra formulalogarithmsDetailThe logarithm is the inverse of exponentiation.Explore the ideaFound an error? Contact us.Related formulasRelatedExponential functionf(x)=ax,a>0, a≠1f(x)=a^x,\quad a>0,\;a\ne1f(x)=ax,a>0,a=1Open formulaOpen in sectionRelatedLogarithm of a productlogb(xy)=logbx+logby\log_b(xy)=\log_bx+\log_bylogb(xy)=logbx+logbyOpen formulaOpen in section