Question

The correct statement(s) among the following is/are

• A. The value of ${\log }_3\left({\log }_{4}65\right)$ is greater than $1$
• B. The value of ${\log }_{0.4}0.3$ is less than $1$
• C. The value of ${\log }_{0.999}1.999$ is positive
• D. The value of ${\log }_{0.6}0.98$ is negative

Answer 1

The correct option is A The value of ${\log }_3\left({\log }_{4}65\right)$ is greater than $1$

${\log }_3\left({\log }_{4}65\right)$


Here $a=3,x={\log }_{4}65$
$x={\log }_{4}65={\log }_4(64+1)\Rightarrow x>3(\because {\log }_{4}64=3)$
$\therefore {\log }_3\left({\log }_{4}65\right)>1$

${\log }_{0.4}0.3$


Here, $a=0.3,x=0.4$
$\therefore {\log }_{0.4}0.3>1$

${\log }_{0.999}1.999$


Here, $a=0.999,x=1.999$
$\therefore {\log }_{0.999}1.999<0$

${\log }_{0.6}0.98$


Here, $a=0.6,x=0.98$
$\therefore {\log }_{0.6}0.98>0$