Question

помогите решить логорифмы

Answer 1

Вычислить.

Задание #5

$log_2\dfrac{1}{\sqrt[6]{128}} = log_2\dfrac{1}{\sqrt[6]{2^7}} = log_2\dfrac{1}{2^{\frac{7}{6}}} = log_22^{-\frac{7}{6}} = -\dfrac{7}{6}log_22 = -\dfrac{7}{6}.$

Задание #6

$2log_\frac{1}{3}6 - \dfrac{1}{2}log_\frac{1}{3}400 + 3log_{\frac{1}{3}}\sqrt[3]{45} = log_{\frac{1}{3}}6^2 - log_{\frac{1}{3}}400^{\frac{1}{2}} + log_{\frac{1}{3}}\left(\sqrt[3]{45}\right)^3 =\\\\= log_\frac{1}{3}36 - log_{\frac{1}{3}}20 + log_{\frac{1}{3}}45 = log_{\frac{1}{3}}\left(\dfrac{36\cdot45}{20}\right) = log_{\frac{1}{3}}(9\cdot9) =\\\\= log_{\frac{1}{3}}3^4 = log_{\frac{1}{3}}\left(\dfrac{1}{3^4}\right)^{-1} = log_{\frac{1}{3}}\left(\dfrac{1}{3}\right)^{-4} = -4log_\frac{1}{3}\dfrac{1}{3} = -4.$