Bài 3 trang 38 SGK Toán 11 Tập 2 Cánh diều - CD

a) Ta có: log_a(a²b³) = log_aa² + log_ab³ = 2log_aa + 3log_ab = 2 . 1 + 3 . 2 = 8;

b) Ta có: ${\log }_a\frac{a\sqrt{a}}{b\sqrt[3]{b}}={\log }_a{\left(\sqrt{a}\right)}^3-{\log }_a{\left(\sqrt[3]{b}\right)}^4={\log }_a{a}^{\frac{3}{2}}-{\log }_a{b}^{\frac{4}{3}}$

$=\frac{3}{2}{\log }_{a}a-\frac{4}{3}{\log }_{a}b=\frac{3}{2}\cdot 1-\frac{4}{3}\cdot 2=\frac{3}{2}-\frac{8}{3}=-\frac{7}{6};$

c) Ta có: ${\log }_a\left(2b\right)+{\log }_a\left(\frac{b^2}{2}\right)={\log }_a\left(2b\cdot \frac{b^2}{2}\right)={\log }_a{b}^3=3{\log }_{a}b=3\cdot 2=6.$

-- Mod Toán 11 HỌC247