obliczyć logarytmy

[razelll]

obliczyć:

\(\displaystyle{ ( \sqrt[3]{4} ) ^{log _{4 \sqrt{2} } } ^{32}}\)


\(\displaystyle{ 3 ^{1-log _{3} } ^{2}}\)

oblicz wiedząć, że \(\displaystyle{ a=log _{3}2}\)
\(\displaystyle{ b=log _{3} 5}\)


\(\displaystyle{ a)log _{3}20}\)


\(\displaystyle{ b)log _{3} \frac{2}{25}}\)


\(\displaystyle{ c)log _{3}3 \frac{1}{8}}\)


\(\displaystyle{ d)log _{3} \sqrt{10}}\)


\(\displaystyle{ e)log _{3}0,2 \sqrt{2}}\)


\(\displaystyle{ f)log _{3}100}\)

[Andreas]

a) \(\displaystyle{ \log_3 20 =\log_3 (2 \cdot 2 \cdot 5) = \log_3 2 + \log_3 2 + \log_3 5= 2a+b}\)

d) \(\displaystyle{ \log_3 \sqrt {10} = \log_3 (2 \cdot 5)^{1/2}=...}\)

[Muchomorek]

\(\displaystyle{ c)log _{3}3 \frac{1}{8}=log _{3}\frac{25}{8}=log _{3}\frac{5^2}{2^3}=log _{3}{5^2}-log _{3}{2^3}=2log _{3}{5}-3log _{3}{2}=2b-3a}\)