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Dekadni logaritam

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dekadni logaritam x y = log x 0 10 101 1 3,2 100,5 0,5 1 100
$$ \begin{aligned} & \log x = \log_{10} x \\ \\ & y = \log x \ \Longleftrightarrow \ x = 10^y \end{aligned} $$

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Formule

dekadni logaritam

$$ \log x = \log_{10} x $$
$$ y = \log x \ \Longleftrightarrow \ x = 10^y $$
$$ \begin{aligned} \log x &= \frac{\log_a x}{\log_a 10} = \frac{\ln x}{\ln 10} \\ \\ \log x &= \frac{1}{\log_x 10} \end{aligned} $$
$$ \begin{aligned} & \log\left(x\cdot z\right) = \log x + \log z \\ \\ & \log\left(\frac{x}{z}\right) = \log x - \log z \end{aligned} $$
$$ \begin{aligned} \log 1 &= 0 \\ \\ \log 10 &= 1 \end{aligned} $$
$$ \begin{aligned} & \log x^r = r\cdot\log x \\ \\ & \log 10^r = r \\ \\ & 10^{\log x} = \log 10^x = x \end{aligned} $$

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