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Logarithmic Inequalities - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
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EASYSolve for C, $log_{0.2}(C+5)>0$
The value of $m, \log _e(m-3)<1$ is
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Logarithmic Inequalities
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.
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