Question

ХЕЛП!!!!

Вычили:

Найди log15 5,если log15 27 = b

Answer 1

Ответ:

$log_{15}(27) = b \\ log_{15}( {3}^{3} ) = b \\ 3 log_{15}(3) = b \\ \frac{3}{ log_{3}(15) } = b \\ \frac{3}{ log_{3}(3 \times 5) } = b \\ \frac{3}{ log_{3}(3) + log_{3}(5) } = b \\ \frac{3}{1 + log_{3}(5) } = b \\ 1 + log_{3}(5) = \frac{3}{b} \\ log_{3}(5) = \frac{3}{b} - 1$

$log_{15}(5) = \frac{1}{ log_{5}(15) } = \frac{1}{ log_{5}(5) + log_{5}(3) } = \frac{1}{ 1 + log_{5}(3) } = \frac{1}{1 + \frac{1}{ log_{3}(5) } }$

$\frac{1}{1 + \frac{1}{ log_{3}(5) } } = \frac{1}{1 + \frac{1}{ \frac{3}{b} - 1} } = \frac{1}{1 + \frac{b}{3 - b} } = \frac{1}{ \frac{3 - b + b}{3 - b} } = \frac{3 - b}{3} = 1 - \frac{b}{3}$

Ответ: 1 - b/3.

как-то так