Question

Найдите значения выражений А)
Б)
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${3}^{2 - log_{3}5 } + ( \frac{1}{3} ) ^{ log_{3}5 }$
${9}^{3 - log_{3}54 } + {7}^{ - log_{7}2}$

Answer 1

$A)\ \ \displaystyle 3^{2-log_35}+\Big(\frac{1}{3}\Big)^{log_35}=3^2\cdot \frac{1}{3^{log_35}}+\frac{1}{3^{log_35}}=\frac{9}{5}+\frac{1}{5}=\frac{10}{5}=2\\\\\\\\B)\ \ 9^{3-log_354}+7^{-log_72}=9^3\cdot \frac{1}{9^{log_354}}+\frac{1}{7^{log_72}}=\frac{9^3}{3^{2log_354}}+\frac{1}{2}=\\\\\\=\frac{9^3}{3^{log_3(54^2)}}+\frac{1}{2}=\frac{9^3}{54^2}+\frac{1}{2}=\frac{9^3}{(9\cdot 6)^2}+\frac{1}{2}=\frac{9^3}{9^2\cdot 6^2}+\frac{1}{2}=\frac{9}{6^2}+\frac{1}{2}=\\\\\\=\frac{1}{4}+\frac{1}{2}=\frac{3}{4}$