Задание 4.14

Question

4.14. Вычислите:
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1) $3^{\log _{3} \frac{1}{27}}\qquad$
3) $4^{\log _{2} 9}\qquad\qquad$
5) $10^{{2}+\lg 8}$;
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2) $5^{\frac{1}{2} \log _{5} 49}\quad$
4) $\left(\frac{1}{9}ight)^{-2 \log _{3} 12}\qquad$
6) $\left(\frac{1}{2}ight)^{\log _{\frac{1}{2}} 6-3}$.

Gimli · Accepted Answer

1) $3^{\log _{3} \frac{1}{27}}=\frac{1}{27}$
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3) $4^{\log _{2} 9}=2^{2\log _{2} 9}=9^{2}=81$
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5) $10^{{2}+\lg 8}=10^{2} 	imes 10^{lg8}=100 	imes 8=800$
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2) $5^{\frac{1}{2} \log _{5} 49}=49^{\frac{1}{2}}=7$
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4) $\left(\frac{1}{9}ight)^{-2 \log _{3} 12}=3^{4 \log _{3} 12}=12^{4}$
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6) $\left(\frac{1}{2}ight)^{\log _{\frac{1}{2}} 6-3}=\left(\frac{1}{2}ight)^ {\log _{\frac{1}{2}}6}:\left(\frac{1}{2}ight)^{3}=6 	imes 8=48$.

Задание 4.14

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Задание 4.14

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