Question

rút gọn biểu thức

a) \(\log_2\left(2^3.2^4:2^{-3}\right)\)

b) \(\log_a2+\log_a12-\log_26\)

c) \(\log_{a^2}x+\log_ax^3\)

d)\(\log_a\sqrt{x^2\sqrt[3]{x\sqrt{x}}}\)

Answer 1

a: \(log_2\left(2^3\cdot2^4:2^{-3}\right)\)

\(=log_2\left(2^{7-\left(-3\right)}\right)\)

\(=log_2\left(2^{10}\right)\)

=10

b: \(log_a2+log_a12-log_26\)

\(=log_a\left(2\cdot12\right)-log_26\)

\(=log_a24-log_26\)

c: \(log_{a^2}x+log_ax^3\)

\(=\dfrac{1}{2}\cdot log_ax+3\cdot log_ax\)

\(=\dfrac{7}{2}\cdot log_ax\)

d: \(log_a\sqrt{x^2\cdot\sqrt[3]{x\sqrt{x}}}\)

\(=log_a\left(x^2\cdot\sqrt[3]{x^{\dfrac{3}{2}}}\right)^{\dfrac{1}{2}}\)

\(=log_a\left(x^2\cdot x^{\dfrac{1}{3}}\right)^{\dfrac{1}{2}}=log_ax^{\dfrac{7}{3}\cdot\dfrac{1}{2}}=log_ax^{\dfrac{7}{6}}=\dfrac{7}{6}\cdot log_ax\)