Logarithmic Inequalities - Practice Questions & MCQ

Logarithmic inequalities:

$\begin{aligned} & \log _a x>\log _a y=\left\{\begin{array}{lc}x>y, & \text { if } a>1 \\ x<y, & \text { if } 0<a<1\end{array}\right. \\ & \log _a x>y= \begin{cases}x>a^y, & \text { if } a>1 \\ x<a^y, & \text { if } 0<a<1\end{cases} \\ & \log _a x<y= \begin{cases}x<a^y, & \text { if } a>1 \\ x>a^y, & \text { if } 0<a<1\end{cases} \end{aligned}$

So, we change the sign of inequality while removing the log when the base is less than 1

Note: We always take the intersection of the answer of this inequality with the domains of all the log terms involved in the inequality.