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Logaritmy

Kalkulačky

Vzorce

$$ \begin{aligned} &\bullet\ y = \log_a x \ \Longleftrightarrow \ a^y = x \\ \\ \\ &\bullet\ \log x = \log_{10} x \\ \\ &\bullet\ \ln x = \log_e x \\ \\ &\bullet\ e \doteq 2,72 \end{aligned} $$
$$ \begin{aligned} &\bullet\ \log_a x = \frac{\log_b x}{\log_b a} = \frac{\log x}{\log a} = \frac{\ln x}{\ln a} \\ \\ &\bullet\ \log_a x = \frac{1}{\log_x a} \\ \\ &\bullet\ \log_a (x \cdot z) = \log_a x + \log_a z \\ \\ &\bullet\ \log_a \frac{x}{z} = \log_a x - \log_a z \end{aligned} $$
$$ \begin{aligned} &\bullet\ \log_a x^r = r \cdot \log_a x \\ \\ &\bullet\ \log_a a^r = r \\ \\ &\bullet\ a^{\log_a x} = \log_a a^x = x \end{aligned} $$
$$ \begin{aligned} &\bullet\ \log_a 1 = 0 \\ \\ &\bullet\ \log_a a = 1 \\ \\ \end{aligned} $$

Uživatelské hodnocení

4,8/5 (10×)