Ответ:
Cвойствa логарифма:
[tex]\bf log_{a}\, b^{k}=k\cdot log_{a}\, b\ \ ,\ \ log_{a}\, a=1\ \ ,\ \ log_{a^{k}}\, b=\dfrac{1}{k}\cdot log_{a}\, b[/tex]
[tex]\bf a > 0\ ,\ a\ne 1\ ,\ b > 0[/tex] .
[tex]\bf 13.4)\ \ \ log_381=log_33^4=4\cdot log_33=4\cdot 1=4\\\\log_51=log_55^0=0\cdot log_55=0\cdot 1=0\\\\log_264=log_22^6=6\cdot log_22=6\cdot 1=6\\\\ log_5625=log_55^4=4\cdot log_55=4\cdot 1=4[/tex]
[tex]\bf 13.6)\ \ \ log_{\sqrt2}\, 16=log_{2^{\frac{1}{2}}}\, 2^4=4\cdot \dfrac{1}{1/2}\cdot log_22=4\cdot 2\cdot 1=8\\\\log_{\sqrt3}\, 9=log_{3^{\frac{1}{2}}}\, 3^2=2\cdot \dfrac{1}{1/2}\cdot log_33=2\cdot 2\cdot 1=4\\\\log_{3}\, 243=log_{3}\, 3^5=5\cdot log_33=5\cdot 1=5\\\\lg0,1=log_{10}\, 0,1=log_{10}\, 10^{-1}=-1\cdot log_{10}\, 10=-1\cdot 1=-1[/tex]
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Ответ:
Cвойствa логарифма:
[tex]\bf log_{a}\, b^{k}=k\cdot log_{a}\, b\ \ ,\ \ log_{a}\, a=1\ \ ,\ \ log_{a^{k}}\, b=\dfrac{1}{k}\cdot log_{a}\, b[/tex]
[tex]\bf a > 0\ ,\ a\ne 1\ ,\ b > 0[/tex] .
[tex]\bf 13.4)\ \ \ log_381=log_33^4=4\cdot log_33=4\cdot 1=4\\\\log_51=log_55^0=0\cdot log_55=0\cdot 1=0\\\\log_264=log_22^6=6\cdot log_22=6\cdot 1=6\\\\ log_5625=log_55^4=4\cdot log_55=4\cdot 1=4[/tex]
[tex]\bf 13.6)\ \ \ log_{\sqrt2}\, 16=log_{2^{\frac{1}{2}}}\, 2^4=4\cdot \dfrac{1}{1/2}\cdot log_22=4\cdot 2\cdot 1=8\\\\log_{\sqrt3}\, 9=log_{3^{\frac{1}{2}}}\, 3^2=2\cdot \dfrac{1}{1/2}\cdot log_33=2\cdot 2\cdot 1=4\\\\log_{3}\, 243=log_{3}\, 3^5=5\cdot log_33=5\cdot 1=5\\\\lg0,1=log_{10}\, 0,1=log_{10}\, 10^{-1}=-1\cdot log_{10}\, 10=-1\cdot 1=-1[/tex]