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Logarytmy
: 23 cze 2017, 15:03
autor: kitinap
Oblicz:
a)\(\log_525\)
b) \(\log_{\sqrt{2}}8\)
c) \(2\log_48\)
d) \(9^{1-\log_35}\)
e)\(\frac{3\log_{3}2+\log_{3}\frac{81}{8}}{\log 24-\log \frac{12}{5}}\)
Re: Logarytmy
: 23 cze 2017, 15:09
autor: eresh
kitinap pisze:Oblicz:
a)\(\log_525\)
\(\log_525=x\\
5^x=25\\
5^x=5^2\\
x=2\\
\log_525=2\)
Re: Logarytmy
: 23 cze 2017, 15:11
autor: eresh
kitinap pisze:Oblicz:
b) \(\log_{\sqrt{2}}8\)
\(\log_{\sqrt{2}}8=x\\
(\sqrt{2})^x=8\\
2^{\frac{1}{2}x}=2^3\\
\frac{1}{2}x=3\\
x=6\\
\log_{\sqrt{2}}8=6\)
Re: Logarytmy
: 23 cze 2017, 15:11
autor: eresh
kitinap pisze:Oblicz:
c) \(2\log_48\)
\(2\log_48=\log_48^2=\log_464=\log_44^3=3\log_44=3\)
Re: Logarytmy
: 23 cze 2017, 15:13
autor: eresh
kitinap pisze:Oblicz:
d) \(9^{1-\log_35}\)
\(9^{1-\log_35}=9^1\cdot 9^{-\log_35}=9\cdot 9^{\log_3\frac{1}{5}}=9\cdot 3^{2\log_3\frac{1}{5}}=9\cdot 3^{\log_3\frac{1}{25}}=9\cdot \frac{1}{25}=\frac{9}{25}\)
Re: Logarytmy
: 23 cze 2017, 15:15
autor: eresh
kitinap pisze:Oblicz:
e)\(\frac{3\log_{3}2+\log_{3}\frac{81}{8}}{\log 24-\log \frac{12}{5}}\)
\(\frac{3\log_{3}2+\log_{3}\frac{81}{8}}{\log 24-\log \frac{12}{5}}=\frac{\log_38+\log_3\frac{81}{8}}{\log (24\cdot\frac{5}{12})}=\frac{\log_381}{\log 10}=\frac{4}{1}=4\)
Re: Logarytmy
: 23 cze 2017, 15:40
autor: korki_fizyka
kitinap pisze:Oblicz:
a)\(\log_525\)
b) \(\log_{\sqrt{2}}8\)
c) \(2\log_48\)
d) \(9^{1-\log_35}\)
e)\(\frac{3\log_{3}2+\log_{3}\frac{81}{8}}{\log 24-\log \frac{12}{5}}\)
chłopaku ! nie masz kalkulatora lub karty wzorów z logarytmami
