Biểu thức \(\log_a\left(\frac{a^2.\sqrt[3]{a^2}.\sqrt[5]{a^2}}{\sqrt[7]{a^{12}}}\right)\) rút gọn bằng
\(\dfrac{149}{60}\). \(\dfrac{46}{15}\). \(\dfrac{142}{105}\). \(\dfrac{8}{3}\). Hướng dẫn giải:\(\log_a\left(\frac{a^2.\sqrt[3]{a^2}.\sqrt[5]{a^2}}{\sqrt[7]{a^{12}}}\right)=\log_a\left(\frac{a^2.a^{\frac{2}{3}}.a^{\frac{2}{5}}}{a^{\frac{12}{7}}}\right)=\log_aa^{2+\frac{2}{3}+\frac{2}{5}-\frac{12}{7}}\)
\(=\log_aa^{\frac{142}{105}}=\dfrac{142}{105}\).