# Oversikt: Potenser og logaritmer

# Formler

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gutter: 2
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**Potensregler**
^^^
$$
\begin{align*}
    x^{p} \cdot x^q &= x^{p+q} \\
    \\
    \dfrac{x^{p}}{x^q} &= x^{p-q} \\
    \\
    (x^p)^q &= x^{p \cdot q} \\
    \\
    x^0 &= 1 \\
    \\
    x^{-p} &= \dfrac{1}{x^p} \\
\end{align*}
$$

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::::::{grid-item-card}
**Logaritmeregler**
^^^
$$
\begin{align*}
    x &= \log_a y \liff y = a^x \\
    \\
    \log_a(xy) &= \log_a x + \log_a y \\
    \\
    \log_a\left(\dfrac{x}{y}\right) &= \log_a x - \log_a y \\
    \\
    \log_a(x^p) &= p \cdot \log_a x \\
    \\
    \log_a 1 &= 0 \\
\end{align*}
$$


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