I'm Kalle from Finland.
I use these when editing Wikipedia.
a b + c = a b a c {\displaystyle a^{b+c}=a^{b}a^{c}}
a b − c = a b a c {\displaystyle a^{b-c}={\frac {a^{b}}{a^{c}}}}
a − b = 1 a b {\displaystyle a^{-b}={\frac {1}{a^{b}}}}
( a b ) c = a c b c {\displaystyle (ab)^{c}=a^{c}b^{c}}
( a b ) c = a c b c {\displaystyle \left({\frac {a}{b}}\right)^{c}={\frac {a^{c}}{b^{c}}}}
( a b ) c = a b c {\displaystyle (a^{b})^{c}=a^{bc}}
a = c b ⇔ a b = c {\displaystyle a={\sqrt[{b}]{c}}\ \Leftrightarrow \ a^{b}=c}
a b = a 1 b {\displaystyle {\sqrt[{b}]{a}}=a^{\frac {1}{b}}}
b = log a c ⇔ a b = c {\displaystyle b=\log _{a}c\ \Leftrightarrow \ a^{b}=c}
log a b = log a + log b {\displaystyle \log ab=\log a+\log b}
log a b = log a − log b {\displaystyle \log {\frac {a}{b}}=\log a-\log b}
log a b = b ⋅ log a {\displaystyle \log a^{b}=b\cdot \log a}
log a b = log a b {\displaystyle \log {\sqrt[{b}]{a}}={\frac {\log a}{b}}}
log b a = log a log b {\displaystyle \log _{b}a={\frac {\log a}{\log b}}}
For a x 2 + b x + c = 0 {\displaystyle ax^{2}+bx+c=0} : x = − b ± b 2 − 4 a c 2 a {\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
Common expressions (see page source):
See also: Help:Displaying_a_formula#Formatting_using_TeX
![{\displaystyle a={\sqrt[{b}]{c}}\ \Leftrightarrow \ a^{b}=c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c41465cff2f4d98707b1e776e3f38040d1c3534f)
![{\displaystyle {\sqrt[{b}]{a}}=a^{\frac {1}{b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d253426457abed2ba2228bdaecd253b25a99ec2a)
![{\displaystyle \log {\sqrt[{b}]{a}}={\frac {\log a}{b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dcf6d4a7074ec0eaad7c8f70dd3771ef67c9d14d)
: 
![{\displaystyle a^{b},a^{bc},a_{1},a_{10},{\sqrt {a}},{\sqrt[{b}]{a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cbb49d609d2b12f81c3408719d20a2f3f18253e)
(space, degree sign, text)