Задание 4.24

Question

4.24. Вычислите:
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1) $\log _{9} \log _{\frac{1}{5}} \frac{1}{125}\qquad$;
3) $\log _{6} \operatorname{tg} 225^{\circ} ;$
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2) $\log _{\frac{1}{3}} \log _{4} 64\qquad$
4) $\log _{\sqrt{3}} \operatorname{tg} \frac{\pi}{6}$.
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Gimli · Accepted Answer

$$
\begin {array}
	ext { 1) } \log _{9} \log _{\frac{1}{5}} \frac{1}{125}=\log _{3} 3=1\
	ext { 2) } \log _{\frac{1}{3}} \log _{4} 64=\log _{\frac{1}{3}} 3=\log _{(3)^{-1}} 3=\frac{1}{-1} \log _{3} 3=-1 .\
3) \log _{6} \operatorname{tg} 225^{\circ}=\log _{6} \operatorname{tg}\left(-135^{\circ}ight)=\log _{6}\left(-\operatorname{tg} 135^{\circ}ight)=\log _{6}(-(-1))=\log _{6} 1=0\
4) \log _{\sqrt{3}} \operatorname{tg} \frac{\pi}{6}=\log _{\sqrt{3}} \frac{\sqrt{3}}{3}=\log _{\sqrt{3}} \frac{1}{\sqrt{3}}=\log _{\sqrt{3}}(\sqrt{3})^{-1}=-1\
\end{array}
$$

Задание 4.24

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Задание 4.24

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