Question

Логарифмы.
Спасибо заранее!

Answer 1

Ответ:

1.

$log_{a}(a) = 1 \\ log_{a}(1) = 0 \\ log_{a}( {a}^{5} ) = 5 \\ log_{a}( \frac{1}{a} ) = - 1 \\ log_{a}( \sqrt{a} ) = \frac{1}{2} = 0.5 \\ log_{a}( \sqrt[5]{ {a}^{3} } ) = \frac{3}{5} = 0.6$

2.

$log_{ \frac{1}{2} }( \frac{1}{4} ) = 2 \\ log_{ \frac{1}{2} }(2) = - 1 \\ log_{ \frac{1}{2} }(1) = 0 \\ log_{ \frac{1}{2} }(8) = - 3 \\ log_{ \frac{1}{2} }( \sqrt{2} ) = log_{ {2}^{ - 1} }( {2}^{ \frac{1}{2} } ) = - \frac{1}{2} = - 0.5 \\ log_{ \frac{1}{2} }( \frac{ \sqrt{2} }{2} ) = log_{ {2}^{ - 1} }( {2}^{ \frac{1}{2} - 1 } ) = - 1 \times log_{2}( {2}^{ \frac{ - 1}{2} } ) = \frac{1}{2} = 0.5$

3.

$log_{3}(27) = 3 \\ log_{3}( \frac{1}{9} ) = - 2 \\ log_{9}( \frac{1}{27} ) = log_{ {3}^{2} }( {3}^{ - 3} ) = \frac{1}{2} \times ( - 3) \times log_{3}(3) = - \frac{3}{2} = - 1.5 \\ log_{2}( \sqrt{2} ) = \frac{1}{2} = 0.5 \\ log_{ \sqrt{2} }(4) = 4 \\ log_{ \sqrt{5} }( \sqrt[4]{125} ) = log_{ {5}^{ \frac{1}{2} } }( \sqrt[4]{ {5}^{3} } ) = 2 log_{5}( {5}^{ \frac{3}{4} } ) = 2 \times \frac{3}{4} log_{5}(5) = 1.5$