[tex]\huge \boxed{log_{a}b = c \: gdy \: {a}^{c} = b}[/tex]
e)
[tex]log_{5} \sqrt{5} = x \\ {5}^{x} = \sqrt{5} \\ {5}^{x} = {5}^{ \frac{1}{2} } \\ \boxed{ x = \frac{1}{2} }[/tex]
f)
[tex]log_{5} \sqrt[3]{5} = x \\ {5}^{x} = \sqrt[3]{5} \\ {5}^{x} = {5}^{ \frac{1}{3} } \\ \boxed{ x = \frac{1}{3}}[/tex]
g)
[tex]log_{5}\sqrt[5]{5} = x \\ {5}^{x} = \sqrt[5]{5} \\ {5}^{x} = {5}^{ \frac{1}{5} } \\ \boxed{x = \frac{1}{5} }[/tex]
h)
[tex]log_{5}\frac{1}{5 \sqrt{5} } = x \\ {5}^{x} = \frac{1}{5 \sqrt{5} } \\ {5}^{x} = \frac{1}{ {5}^{1} \times {5}^{ \frac{1}{2} } } \\ {5}^{x} = \frac{1}{ {5}^{ \frac{3}{2} } } \\ {5}^{x} = {5}^{ - \frac{3}{2} } \\ \boxed{x = - \frac{3}{2} }[/tex]
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Korzystamy z następującego wzoru na logarytmy:
[tex]\huge \boxed{log_{a}b = c \: gdy \: {a}^{c} = b}[/tex]
e)
[tex]log_{5} \sqrt{5} = x \\ {5}^{x} = \sqrt{5} \\ {5}^{x} = {5}^{ \frac{1}{2} } \\ \boxed{ x = \frac{1}{2} }[/tex]
f)
[tex]log_{5} \sqrt[3]{5} = x \\ {5}^{x} = \sqrt[3]{5} \\ {5}^{x} = {5}^{ \frac{1}{3} } \\ \boxed{ x = \frac{1}{3}}[/tex]
g)
[tex]log_{5}\sqrt[5]{5} = x \\ {5}^{x} = \sqrt[5]{5} \\ {5}^{x} = {5}^{ \frac{1}{5} } \\ \boxed{x = \frac{1}{5} }[/tex]
h)
[tex]log_{5}\frac{1}{5 \sqrt{5} } = x \\ {5}^{x} = \frac{1}{5 \sqrt{5} } \\ {5}^{x} = \frac{1}{ {5}^{1} \times {5}^{ \frac{1}{2} } } \\ {5}^{x} = \frac{1}{ {5}^{ \frac{3}{2} } } \\ {5}^{x} = {5}^{ - \frac{3}{2} } \\ \boxed{x = - \frac{3}{2} }[/tex]