Cho $\Large a=\log_{2}5, b=\log_{5}3, \log_{30}150=\dfrac{x.a.b+y.a+z.

Cho $\Large a=\log_{2}5, b=\log_{5}3, \log_{30}150=\dfrac{x.a.b+y.a+z.b+1}{m.a.b+n.a+p.b+q}$ ($\Large x$, $\Large y$, $\Large z$, $\Large m$, $\Large n$, $\Large p$, $\Large q$ là các số nguyên ). Tính $\Large x+y+z+m+n+p+q$
 

• A.

  A. 5

• B.

  B. 4

• C.

  C. 6

• D.

  D. 1

Chọn C

Ta có: 

$\Large \begin{align}&\log_{30}150=\dfrac{\log_{5}150}{\log_{5}30}=\dfrac{\log_{5}5+\log_{5}3+\log_{5}2+\log_{5}5}{\log_{5}5+\log_{5}3+\log_{5}2}\\&=\dfrac{2+b+\dfrac{1}{a}}{1+b+\dfrac{1}{a}}=\dfrac{ab+2a+1}{ab+a+1}\end{align}$

Khi đó:, $\Large x=1, y=2, z=0, m=1, n=1, p=0, q=1$, suy ra $\Large x+y+z+m+n+p+q=6$