Question

я буду очень вам благодарен

Answer 1

7.

$log_{3}(2) - log_{3}(2) \times log_{2}(6) + log_{3}(6) = \\ = log_{3}(2 \times 6) - \frac{1}{ log_{2}(3) } \times log_{2}(6) = \\ = log_{3}(12) - log_{3}(6) = \\ = log_{3}(2)$

ответ: а

8.

$log_{9}(17) \times log_{17}(7) \times log_{49}(9) = \\ = \frac{ log_{17}(7) }{ log_{17}(9) } \times log_{49}(9) = \\ = log_{9}(7) \times log_{49}(9) = \\ = \frac{ log_{9}(7) }{ log_{9}(49) } = log_{49}(7) = \frac{1}{2}$

ответ: а

9.

$log_{5}(72) = log_{5}(2 \times {6}^{2} ) = log_{5}(2 \times {2}^{2} \times {3}^{2} ) = \\ = log_{5}( {2}^{3} ) + log_{5}( {3}^{2} ) = \\ = 3 log_{5}(2) + 2 log_{5}(3) = \\ \\ = 3a + 2b$

ответ: а

10.

$lg7( log_{7}(15) + log_{7}(4) - log_{7}(6)) = \\ = lg7 \times log_{7}( \frac{15 \times 4}{6} ) = \\ = log_{10}(7) \times log_{7}(10) = 1$

ответ: в