Question

If ${\log }_{m}3>2\&3<m^2,$ then which of the following can be true?

• A. $2.7$
• B. $0.7$
• C. $2$
• D. $1.7$

Answer 1

The correct option is B $0.7$

Given that ${\log }_{m}3>2\&3<m^2$

Using the property
${\log }_{m}a>b\Rightarrow \{\begin{array}{cc}a>m^b,& \text{if}m>1\\ a<m^b,& \text{if}0<m<1\end{array}$

Here, ${\log }_{m}3>2\&3<m^2\Rightarrow 0<m<1$
Hence, $m$ can be $0.7$ from the given options.