Cho $a > 0, b > 0,$ nếu viết ${{\log }_{3}}{{\left(\sqrt[5]{{{a}^{3}}b} \right)}^{\dfrac{2}{3}}}=\dfrac{x}{5}{{\log }_{3}}a+\dfrac{y}{15}{{\log...

The Collectors · 29/5/21

Câu hỏi: Cho

a > 0, b > 0,

nếu viết

\log_{3} {(\sqrt[5]{a^{3} b})}^{\frac{2}{3}} = \frac{x}{5} \log_{3} a + \frac{y}{15} \log_{3} b

thì

x + y

bằng bao nhiêu?
A. 5.
B. 2.
C. 4.
D. 3.

Ta có

\log_{3} {(\sqrt[5]{a^{3} b})}^{\frac{2}{3}} = \frac{2}{3} . \frac{1}{5} \log_{3} (a^{3} b)

= \frac{2}{15} (\log_{3} a^{3} + \log_{3} b)

= \frac{2}{15} .3 . \log_{3} a + \frac{2}{15} \log_{3} b

= \frac{2}{5} \log_{3} a + \frac{2}{15} \log_{3} b .

Vậy

x = 2, y = 2 \Rightarrow x + y = 4.

Đáp án C.

Cho a>0,b>0, nếu viết ${{\log }_{3}}{{\left(\sqrt[5]{{{a}^{3}}b} \right)}^{\dfrac{2}{3}}}=\dfrac{x}{5}{{\log }_{3}}a+\dfrac{y}{15}{{\log...