I came upon an inequality :-
$\left(\frac{1}{2}\right)^∞<\left(\frac{1}{2}\right)^x<\left(\frac{1}{2}\right)^{-2}$
Then the writer wrote:-
Since , $\frac{1}{2}<1$ ,$$-2<x<∞$$
Please explain me clearly how he did this ?
2026-03-30 14:37:28.1774881448
How is this change possible?
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Take the logarithm of all terms. We can do this since log is a monotonic increasing function. Since $\frac{1}{2}<1$, its logarithm is negative, which causes the direction of the inequalities to flip.