Zadanie Oblicz A) log 5 5 , Log 7 1 , log 5 5 do 3, log 8 8 do 1/3, log 10, log 0,1, log 10 do 5, log 1000,log pierwiastek z 10, log 3 pierwiastek z 3, log 1/2 2, log 1/3 9, log 6 1/36
źródło: Matematyka z plusem liceum/technikum 2 klasa
log_55=1 log_71=0 log_5(5^3)=3 log_8(8^{\frac{1}{3} } )=\frac{1}{3} log10=1 log0,1=log\frac{1}{10}=-1 log10^5=5 log1000=3 log\sqrt10=log10^\frac{1}{2}=\frac{1}{2} log_3\sqrt3=\frac{1}{2} log_{\frac{1}{2}}2=-1 log_{\frac{1}{3}}9=-2 log_6(\frac{1}{36})=-2
A) log 5 5 , Log 7 1 , log 5 5 do 3, log 8 8 do 1/3, log 10, log 0,1, log 10 do 5, log 1000,log pierwiastek z 10, log 3 pierwiastek z 3, log 1/2 2, log 1/3 9,
log_6 \frac{1}{36}=x
6^x=\frac{1}{6^2}
6^x=6^{-2}
x = -2
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A) log_5 5=1, bo 5^1=5
log_7 1=0, bo 7^0=1 … log_55^3=x
5^x=5^3
x = 3 … log_88^{\frac{1}{3}}=x 8^x=8^{\frac{1}{3}} x = 1/3 … log 10 = 1 … log 0,1 10^x=\frac{1}{10} 10^x=10^{-1} x = -1 … log 10^5=5 … log 1000=3 … log \sqrt{10}=\frac{1}{2}
log_3\sqrt3=x
3^x=\sqrt3 3^x=3^{\frac{1}{2}} x = 1/2 … log_{\frac{1}{2}}2=x
(\frac{1}{2})^x=2^1 nie wpisujemy potęgi 1
(\frac{1}{2})^x=(\frac{1}{2})^{-1} x = -1 … log_{ \frac{1}{3}}9=x
(\frac{1}{3})^x=3^2
(\frac{1}{3})^x=(\frac{1}{3^2})^{-2} x = -2 … log_6 \frac{1}{36}=x
6^x=6^{-2} x = -2