Oblicz wartość logarytmu

[Dzobert]

Wiedząc, że \(\displaystyle{ a = \log_{14}2}\) i \(\displaystyle{ b = \log_{14}5}\) oblicz \(\displaystyle{ \log_{7}50}\).

[soku11]

\(\displaystyle{ log_7 50=
\frac{log_{14} 50}{log_{14} 7}=
\frac{log_{14} (5^2\cdot 2)}{log_{14} (14:2)}=
\frac{ log_{14} 5^2+log_{14} 2 }{log_{14} 14-log_{14} 2}=
\frac{2 log_{14} 5+log_{14} 2 }{1-log_{14} 2}=\frac{2b+a}{1-a}}\)

POZDRO

[Dzobert]

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