Вычислить:

[tex] log_{2}(7) \times log_{5}(8) \times \frac{lg25}{lg343} [/tex]
​

Ответ:

[tex] log_{2}(7) \times log_{5}(8) \times \frac{lg(25)}{lg(343)} = \\ = log_{2}(7) \times log_{5}(8) \times log_{343}(25) = \\ = log_{2}(7) \times log_{5}(8) \times log_{ {7}^{3} }( {5}^{2} ) = \\ = log_{2}(7) \times log_{5}(8) \times \frac{2}{3} log_{7}(5) = \\ = \frac{2}{3} \times \frac{1}{ log_{7}(2) } \times log_{7}(5) \times log_{5}(8) = \\ = \frac{2}{3} \times log_{2}(5) \times log_{5}( {2}^{3} ) = \\ = \frac{2}{3} \times 3 \times log_{2}(5) \times log_{5}(2) = 2[/tex]