User:Qalle2

I'm Kalle from Finland.

Math notes

I use these when editing Wikipedia.

Exponents, roots and logarithms

${\displaystyle a^{b}a^{c}=a^{b+c},\ {\frac {a^{b}}{a^{c}}}=a^{b-c}}$

${\displaystyle a^{c}b^{c}=(ab)^{c},\ {\frac {a^{c}}{b^{c}}}=\left({\frac {a}{b}}\right)^{c}}$

${\displaystyle (a^{b})^{c}=a^{bc}}$

${\displaystyle {\sqrt[{b}]{a}}=a^{\frac {1}{b}}}$

${\displaystyle a^{b}=c\ \Leftrightarrow \ a={\sqrt[{b}]{c}}\ \Leftrightarrow \ b=\log _{a}c}$

${\displaystyle \log ab=\log a+\log b,\ \log {\frac {a}{b}}=\log a-\log b}$

${\displaystyle \log a^{b}=b\cdot \log a}$

${\displaystyle \log _{b}a={\frac {\log a}{\log b}}}$

${\displaystyle ax^{2}+bx+c=0\ \Leftrightarrow \ x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$

LaTeX ([itex])

Common expressions (see page source):

• ${\displaystyle \exp ,\ln ,\log ,\log _{2},\log _{10},\sin ,\cos ,\tan ,\arcsin ,\arccos ,\arctan }$
• ${\displaystyle \alpha ,\beta ,\gamma ,\delta ,\theta ,\mu ,\pi ,\tau ,\phi ,\varphi ,\omega }$
• ${\displaystyle \times ,\cdot ,\pm ,\ldots ,\approx ,\neq ,\leq ,\geq ,\Leftrightarrow }$
• ${\displaystyle a^{b},a^{bc},a_{1},a_{10},{\sqrt {a}},{\sqrt[{b}]{a}}}$
• ${\displaystyle {\frac {a}{b}},\left({\frac {a}{b}}\right)^{c},{\binom {a}{b}}}$
• ${\displaystyle a\ b}$ (space)