Oversikt: Potenser og logaritmer

Formler

Potensregler

\[\begin{split} \begin{align*} x^{p} \cdot x^q &= x^{p+q} \\ \\ \dfrac{x^{p}}{x^q} &= x^{p-q} \\ \\ (x^p)^q &= x^{p \cdot q} \\ \\ x^0 &= 1 \\ \\ x^{-p} &= \dfrac{1}{x^p} \\ \end{align*} \end{split}\]

Logaritmeregler

\[\begin{split} \begin{align*} x &= \log_a y \liff y = a^x \\ \\ \log_a(xy) &= \log_a x + \log_a y \\ \\ \log_a\left(\dfrac{x}{y}\right) &= \log_a x - \log_a y \\ \\ \log_a(x^p) &= p \cdot \log_a x \\ \\ \log_a 1 &= 0 \\ \end{align*} \end{split}\]