Question

rút gọn các biểu thức, giả sử các biểu thức đều có nghĩa

a) \(G=3log_3a+log_3a^5-log_3a^2\)

b) \(H=log_a\left(a^2.\sqrt[3]{a}.\sqrt{a}\right)\)

c) \(I=log_a\left(a.\sqrt[3]{a.\sqrt{a^2}}\right)\)

Answer 1

a: \(G=3\cdot log_3a+log_3a^5-log_3a^2\)

\(=3\cdot log_3a+5\cdot log_3a-2\cdot log_3a=6\cdot log_3a\)

b: \(H=log_a\left(a^2\cdot\sqrt[3]{a}\cdot\sqrt{a}\right)=log_a\left(a^2\cdot a^{\dfrac{1}{3}}\cdot a^{\dfrac{1}{2}}\right)\)

\(=2+\dfrac{1}{3}+\dfrac{1}{2}=2+\dfrac{5}{6}=\dfrac{17}{6}\)

c: \(H=log_a\left(a\cdot\sqrt[3]{a\cdot\sqrt{a^2}}\right)\)

\(=log_a\left(a\cdot\sqrt[3]{a\cdot a}\right)=log_a\left(a\cdot a^{\dfrac{2}{3}}\right)=\dfrac{5}{3}\)

Answer 2

\(G=3log_3a+5log_3a-2log_3a=6log_3a\)

\(H=log_a\left(a^{\dfrac{17}{6}}\right)=\dfrac{17}{6}log_aa=\dfrac{17}{6}\)

\(I=log_a\left(a^{\dfrac{5}{3}}\right)=\dfrac{5}{3}log_aa=\dfrac{5}{3}\)