Логаритъм

[IvanTBG]

Пресметнете: [tex]log_{49 }[/tex]X, ако Х = ([tex]log_{5 } (2)^{ log_{2 }(125) })^{ log_{3 }7 }[/tex]

[Davids]

$X = \left(\log_5(2^{\log_2125})\right)^{\log_37} = \left(\log_2(125)\log_52\right)^{\log_37} = \left(\frac{\log_2125}{\log_25}\right)^{\log_37} = \left(\log_5125\right)^{\log_37} = 3^{\log_37} = 7$
$\Rightarrow \log_{49}X = \log_{49}7 = \frac{1}{2}$