Question

Каким в местах где есть дроби можно решать эти логарифмы?

Answer 1

есть формула:

$\frac{ log_{c}(a) }{ log_{c}(b) } = log_{b}(a) \\$

$\frac{ log_{2}(3) }{ log_{2}(9) } = log_{9}(3) = \frac{1}{2} = 0.5 \\$

_______________

1.

$lg(40) + lg(25) = lg(40 \times 25) = \\ = lg(1000) = 3$

2.

$log_{ \frac{1}{2} }(28) - log_{ \frac{1}{2} }(7) = log_{ \frac{1}{2} }(\frac{28}{7} ) = \\ = log_{ \frac{1}{2} }(4) = - 2$

3.

0,5

4.

${25}^{ log_{5}(3) } \\ \\ {a}^{ log_{a}(b) } = b \\ \\ {5}^{2 log_{5}(3) } = {5}^{ log_{5}( {3}^{2} ) } = {3}^{2} = 9$

5.

$log_{3}(1) \times log_{4}(16) = 0 \times 2 = 0$

6.

$log_{27}(81) = log_{ {3}^{3} }( {3}^{4} ) = \\ = \frac{1}{3} \times 4 log_{3}(3) = \frac{4}{3}$