Question

If $f\left(x\right)={\log }_{a}x$ is decreasing function, then $a$ is

• A. $<1$
• B. $0<a<1$
• C. $>1$
• D. $>e$

Answer 1

The correct option is B $0<a<1$

$f\left(x\right)={\log }_{a}x$

For $x_2>x_1$

$f\left(x_1\right)>f\left(x_2\right)$ from the figure

Hence, for $0<a<1,f\left(x\right)={\log }_{a}x$ is decreasing function.