Cho hàm số \(y = {\log _a}x\). Nếu \(0 < a < 1\) thì hàm số:

\(\left( {0;1} \right)\)

\(R\)

\(R\backslash \left\{ 0 \right\}\)

\(\left( {0; + \infty } \right)\)

\(y' = {\log _a}x\)

\(y' = x\ln a\)  

\(y' = \dfrac{1}{{x\ln a}}\)

\(y' = \dfrac{1}{x}\ln a\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln \left( {1 + x} \right)}}{x} = 1\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln \left( {1 - x} \right)}}{x} = 1\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln x}}{x} = 1\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln \left( {1 + x} \right)}}{{1 + x}} = 1\)

\(x = 1\)

\(y = 0\)

\(y = 1\)          

\(x = 0\) 

\({y_0} = {\log _a}{x_0}\)

\({y_0} = x_0^a\)       

\({y_0} = {a^{{x_0}}}\)           

\({x_0} = {\log _a}{y_0}\) 

\(\left( {1;0} \right)\)

\(\left( {a,1} \right)\)   

\(\left( {{a^2};a} \right)\)       

\(\left( {{a^2};2} \right)\)