Definition of a logarithm
\[\log_a b=c\Longleftrightarrow a^c=b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0\)
NMT / ZNO
Formulas and reference
A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.
ZNO — full reference
·
Algebra
·
9 formulas
Full ZNO
Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Exponential expressions and logarithms
Logarithms
Logarithm of one
NMT\[\log_a1=0\]
Condition
\(a\gt 0,\ a\ne1\)
Logarithm of the base
NMT\[\log_a a=1\]
Condition
\(a\gt 0,\ a\ne1\)
Fundamental logarithmic identity
NMT\[a^{\log_a b}=b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0\)
Logarithm of a product
NMT\[\log_a(bc)=\log_ab+\log_ac\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0,\ c\gt 0\)
Logarithm of a quotient
NMT\[\log_a\frac bc=\log_ab-\log_ac\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0,\ c\gt 0\)
Logarithm of a power
NMT\[\log_a b^n=n\log_a b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0\)
Logarithm of a root
NMT\[\log_a\sqrt[k]{b}=\frac1k\log_a b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0,\ k\ne0\)
Change of base
\[\log_a b=\frac{\log_c b}{\log_c a}\]
Condition
\(a,b,c\gt 0,\ a\ne1,\ c\ne1\)
No formulas match this search.