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Logarithmic Inequalities - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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23 Questions around this concept.
Solve by difficulty
EASY$\log 24=1.38, \log 54=1.73$ find $\log 36$
Solve for C, $log_{0.2}(C+5)>0$
The value of $m, \log _e(m-3)<1$ is
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Let $x, y$ be real numbers such that $x>2 y>0$ and
$
2 \log (x-2 y)=\log x+\log y
$
Then the possible value (s) of $\frac{x}{y}$
Concepts Covered - 1
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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