Задание 4.13

Question

4.13. Вычислите:
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1) $2^{\log _{2} 32} \quad$
3) $7^{2 \log _{7} 2}\qquad $
5) $\left(\frac{1}{3}ight)^{\log _{5} 6};$
7) $\left(\frac{2}{3}ight)^{\log _{\frac{2}{3}} 8-2}$;
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2) $5^{\log _{5} 0,45}$;
4) $64^{0,5 \log _{2} 12}$;
6) $6^{1+\log _{6} 5}\quad$
8) $6^{\log _{\frac{1}{6}} 3}$.

Gimli · Accepted Answer

\begin{array}{l}
	ext { 1) } 2 ^{\log _{2} 32}=2^{\log _{2} 2^{5}}=2^{5}=32\
	ext { 2) } 5^{\log _{5} 0,45}=0, 45\
	ext { 3) } 7^{2 \log _{7} 2}=2^{2}=4\
	ext { 4) } 64^{0,5 \log _{2} 12}=2^{{3} \log _{2} 12}=12^{3}=1728\
	ext { 5) }\left(\frac{1}{3}ight)^{\log _{3} 6}=3^{-\log _{3} 6}=6^{-1}=\frac{1}{6}\
	ext { 6) } 6^{1+\log _{6} 5}=6^{1} \cdot 6^{\log _{6} 5}=6 \cdot 5=30\
	ext { 7) }\left(\frac{2}{3}ight)^{\log _{\frac{2}{3}} 8-2}=\left(\frac{2}{3}ight)^{\log _{\frac{2}{3}} 8}:\left(\frac{2}{3}ight)^{2}=8 \div \frac{4}{9}=18\
	ext { 8) } 6^{\log _{\frac{1}{6}} 3}=6^{-\log _{\frac{1}{6}} 3}=3^{-1}=\frac{1}{3}\
\end{array}

Задание 4.13

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Задание 4.13

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