Question

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

a) \(D=\dfrac{\left(x^{\sqrt{3}-1}\right)^{1+\sqrt{3}}}{x^{\dfrac{3}{2}}.\sqrt{x}}\)

b) \(E=log_{\dfrac{1}{2}}b^2+log_3b^5-log_3\sqrt{b^5}\)

c) \(F=log_a\left(a^{\dfrac{1}{3}}.\sqrt{a}\right)\)

Answer 1

a: \(D=\dfrac{\left(x^{\sqrt{3}-1}\right)^{1+\sqrt{3}}}{x^{\dfrac{3}{2}}\cdot\sqrt{x}}=\dfrac{x^{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}}{x^{\dfrac{3}{2}}\cdot x^{\dfrac{1}{2}}}=\dfrac{x^{3-1}}{x^2}=1\)

b: \(E=log_{\dfrac{1}{2}}b^2+log_3b^5-log_3\sqrt{b^5}\)

\(=2\cdot log_{\dfrac{1}{2}}b+5\cdot log_3b-log_3b^{\dfrac{5}{2}}\)

\(=2\cdot log_{\dfrac{1}{2}}b+5\cdot log_3b-\dfrac{5}{2}\cdot log_3b\)

\(=2\cdot log_{\dfrac{1}{2}}b+\dfrac{5}{2}\cdot log_3b\)

c: \(F=log_a\left(a^{\dfrac{1}{3}}\cdot\sqrt{a}\right)=log_a\left(a^{\dfrac{1}{3}}\cdot a^{\dfrac{1}{2}}\right)=log_a\left(a^{\dfrac{5}{6}}\right)=\dfrac{5}{6}\)