Nếu logab = 4 thì log a căn b( căn 4của căn a căn b) bằng

10/10

Nếu log_ab = 4 thì $\log_{a \sqrt[3]{b}} (\sqrt[4]{a \sqrt{b}})$ bằng

$\frac{9}{19};$

$\frac{9}{28};$

$\frac{9}{29};$

$\frac{9}{39} .$

Giải thích

Đáp án đúng là: B

$\log_{a \sqrt[3]{b}} (\sqrt[4]{a \sqrt{b}}) = \frac{\log_{a} \sqrt[4]{a \sqrt{b}}}{\log_{a} a \sqrt[3]{b}} = \frac{\log_{a} \sqrt[4]{a b^{\frac{1}{2}}}}{\log_{a} (a b^{\frac{1}{3}})} = \frac{\log_{a} {(a b^{\frac{1}{2}})}^{\frac{1}{4}}}{\log_{a} (a b^{\frac{1}{3}})}$

$= \frac{\log_{a} (a^{\frac{1}{4}} . b^{\frac{1}{2} . \frac{1}{4}})}{\log_{a} (a b^{\frac{1}{3}})} = \frac{\log_{a} (a^{\frac{1}{4}} b^{\frac{1}{8}})}{\log_{a} (a b^{\frac{1}{3}})} = \frac{\log_{a} a^{\frac{1}{4}} + \log_{a} b^{\frac{1}{8}}}{\log_{a} a + \log_{a} b^{\frac{1}{3}}}$

$= \frac{\frac{1}{4} + \frac{1}{8} \log_{a} b}{1 + \frac{1}{3} \log_{a} b} = \frac{\frac{1}{4} + \frac{1}{8} .4}{1 + \frac{1}{3} .4} = \frac{9}{28} .$