Cho \(\log_ab=3;\log_ac=-2\)
1. Với \(x=a^3b^2\sqrt{c}\Rightarrow\log_ax=\log_a\left(a^3b^2\sqrt{c}\right)=\log_aa^3+\log_ab^2+\log_ac^{\frac{1}{2}}\)
\(=3+2.3+\frac{1}{2}\left(-2\right)=8\)
2. Với \(x=\frac{a^4\sqrt[3]{b}}{c^3}\) \(\Rightarrow\log_a\frac{a^4\sqrt[3]{b}}{c^2}=\log_aa^4+\log_ab^{\frac{1}{3}}+\log_ac^3\)
\(=4+\frac{1}{3}\log_ab+3\log_ac=4+\frac{1}{3}.3+3\left(-2\right)=-1\)
3. Với \(x=\log_a\frac{a^2\sqrt[3]{b}c}{\sqrt[3]{a\sqrt{c}}b^3}\Rightarrow\log_a\frac{a^2b^{\frac{1}{3}}c}{a^{\frac{1}{3}}b^3c^{\frac{1}{6}}}=\log_a\frac{a^{\frac{5}{3}}c^{\frac{5}{6}}}{b^{\frac{8}{3}}}=\log_aa^{\frac{5}{3}}-\log_ab^{\frac{8}{3}}+\log_ac^{\frac{3}{2}}\)
\(=\frac{5}{3}-\frac{8}{3}\log_ab+\frac{5}{6}\log_ac=\frac{5}{3}-\frac{8}{3}3+\frac{5}{6}\left(-2\right)=-8\)
