Question

Đề bài

Cho \(a > 0;a \ne 1;{a^{\frac{3}{5}}} = b\)

a)     Viết \({a^6};{a^3}b;\frac{{{a^9}}}{{{b^9}}}\) theo lũy thừa cơ số b

b)    Tính \({\log _a}b;\,{\log _a}\left( {{a^2}{b^5}} \right);\,{\log _{\sqrt[5]{a}}}\left( {\frac{a}{b}} \right)\)

Answer 1

a,Ta có: \(a^6=\left(a^{\dfrac{3}{5}}\right)^{10}=b^{10}\\ a^3b=\left(a^{\dfrac{3}{5}}\right)^5\cdot b=b^5\cdot b=b^6\\ \dfrac{a^9}{b^9}=\dfrac{\left(a^{\dfrac{3}{5}}\right)^{15}}{b^9}=\dfrac{b^{15}}{b^9}=b^6\)

b, \(log_ab=log_aa^{\dfrac{3}{5}}=\dfrac{3}{5}\\ log_a\left(a^2b^5\right)=log_a\left(a^2\cdot a^3\right)=log_a\left(a^5\right)=5\\ log_{\sqrt[5]{a}}\left(\dfrac{a}{b}\right)=5log_a\left(\dfrac{a}{a^{\dfrac{3}{5}}}\right)=5log_a\left(a^{\dfrac{2}{5}}\right)=2\)