Question

Đặt \(\log 2 = a,\log 3 = b\). Biểu thị các biểu thức sau theo \(a\) và \(b\).

a) \({\log _4}9\);                   

b) \({\log _6}12\);                  

c) \({\log _5}6\).

Answer 1

a: \(log_49=\dfrac{log9}{log4}=\dfrac{log3^2}{log2^2}=\dfrac{2\cdot log3}{2\cdot log2}=\dfrac{log3}{log2}=\dfrac{b}{a}\)

b: \(log_612=\dfrac{log12}{log6}=\dfrac{log2^2+log3}{log2+log3}=\dfrac{2\cdot log2+log3}{log2+log3}\)

\(=\dfrac{2a+b}{a+b}\)

c: \(log_56=\dfrac{log6}{log5}=\dfrac{log\left(2\cdot3\right)}{log\left(\dfrac{10}{2}\right)}=\dfrac{log2+log3}{log10-log2}\)

\(=\dfrac{a+b}{1-a}\)