Question

If ${\log }_{m}11>{\log }_{m}33$, then which of the following can be the possible value of $m$ ?

• A. $3$
• B. $6$
• C. $0.6$
• D. $1$

Answer 1

The correct option is C $0.6$

Given: ${\log }_{m}11>{\log }_{m}33$
Now, using the inequality property i.e.
${\log }_{a}x>{\log }_{a}y\Rightarrow (\begin{array}{c}x>y;a>1\\ x<y;0<a<1\end{array}$Here ${\log }_{m}11>{\log }_{m}33\Rightarrow 0<m<1$
Thus the possible values of $m$ is $0.6.$