Question

Вычислите логарифмы, пожалуйста

Answer 1

Ответ:

1

$log_{196}(14) + log_{4}( \frac{1}{64} ) - 3 log_{5}( \sqrt[3]{5} ) = \\ = log_{ {14}^{2} }(14) + log_{4}( {4}^{ - 3} ) - 3 log_{5}( {5}^{ \frac{1}{3} } ) = \\ = \frac{1}{2} - 3 - 3 \times \frac{1}{3} = 0.5 - 3 - 1= - 4 + 0.5 = - 3.5$

2

$log_{24}(6) + log_{24}(8) - \frac{lg(2)}{lg(24)} = \\ = log_{24}(6 \times 8) - log_{24}(2) = \\ = log_{24}( \frac{48}{2} ) = log_{24}(24) = 1$

3

$log_{ \sqrt{3} }(729) + {3}^{1 + \frac{2}{ log_{25}(9) } } = \\ = log_{ {3}^{ \frac{1}{2} } }( {3}^{6} ) + {3}^{1} \times {3}^{2 log_{9}(25) } = \\ = 2 \times 6 + 3 \times {9}^{ log_{9}(25) } = \\ = 12 + 3 \times 25 = 12 + 75 = 87$