Obliczanie logarytmu $\log_5 \dfrac{1}{5\sqrt{5}}$

Ponieważ $\sqrt{5} = 5^{0{,}5}$, to:

$\dfrac{1}{5\sqrt{5}} = \dfrac{1}{5 \times 5^{0{,}5}} = \dfrac{1}{5^{1 + 0{,}5}} = 5^{-1{,}5}$

Zatem $\log_5 \dfrac{1}{5\sqrt{5}} = -1{,}5$.