вправа 3.6 гдз 11 клас математика Нелін Долгова 2019
Вправа 3.6
Умова:
Умова:
Прологарифмуйте вираз за основою 10, якщо ab > 0 і с ≠ 0.
Відповідь ГДЗ:
1) lg|a3b5|c8 = 3lg|a| + 5lg|b| + 8lg|c|. \begin{equation} 2)lg\frac{|\sqrt[3]{ab}|}{c^{2}}= \end{equation} \begin{equation} =\frac{1}{3}lg|a|+\frac{1}{3}lg|b|-2lg|c|. \end{equation} \begin{equation} 3)lg\frac{c^{4}}{(ab)^{\frac{2}{5}}}= \end{equation} \begin{equation} =4lg|c|-\frac{2}{5}lg|a|-\frac{2}{5}lg|b|. \end{equation} \begin{equation} 4)lg100\cdot \sqrt[5]{|ab|c^{2}}= \end{equation} \begin{equation} =lg100+\frac{1}{5}lg|a|+ \end{equation} \begin{equation} +\frac{1}{5}lg|b|+\frac{2}{5}lg|c|= \end{equation} \begin{equation} =2+\frac{1}{5}lg|a|+ \end{equation} \begin{equation} +\frac{1}{5}lg|b|+\frac{2}{5}lg|c|. \end{equation}
1) lg|a3b5|c8 = 3lg|a| + 5lg|b| + 8lg|c|. \begin{equation} 2)lg\frac{|\sqrt[3]{ab}|}{c^{2}}= \end{equation} \begin{equation} =\frac{1}{3}lg|a|+\frac{1}{3}lg|b|-2lg|c|. \end{equation} \begin{equation} 3)lg\frac{c^{4}}{(ab)^{\frac{2}{5}}}= \end{equation} \begin{equation} =4lg|c|-\frac{2}{5}lg|a|-\frac{2}{5}lg|b|. \end{equation} \begin{equation} 4)lg100\cdot \sqrt[5]{|ab|c^{2}}= \end{equation} \begin{equation} =lg100+\frac{1}{5}lg|a|+ \end{equation} \begin{equation} +\frac{1}{5}lg|b|+\frac{2}{5}lg|c|= \end{equation} \begin{equation} =2+\frac{1}{5}lg|a|+ \end{equation} \begin{equation} +\frac{1}{5}lg|b|+\frac{2}{5}lg|c|. \end{equation}