Đặt log x = a, log y = b, log z = c (x, y, z > 0). Hãy biểu thị các biểu thức sau theo a, b, c.

a) log (xyz);           

b) $\log \frac{x^3\sqrt[3]{y}}{100\sqrt{z}}$ ;            

c) log_z (xy²) $(z\ne 1)$ .

a) log(xyz) = log x + log y + log z = a + b + c;

b) $\log \frac{x^3\sqrt[3]{y}}{100\sqrt{z}}=\log \left(x^3\sqrt[3]{y}\right)-\log \left(100\sqrt{z}\right)$

$=\log \left(x^3{y}^{\frac{1}{3}}\right)-\log \left({10}^2{z}^{\frac{1}{2}}\right)$$=3\log x+\frac{1}{3}\log y-2-\frac{1}{2}\log z$

$=3a+\frac{1}{3}b-\frac{1}{2}c-2$

c) ${\log }_z\left(x{y}^2\right)=\frac{\log \left(x{y}^2\right)}{\log z}$

$=\frac{\log xy+2\log }{\log z}=\frac{a+2b}{c}$