I'm studying for the admission test.
In particular, this exponential inequality is a little bit tricky.
this is the inequality:
$$
\left(\frac{2}{e}\right)^x > 1
$$
I've tried to use the change of basis formula to try to solve the logarithm to deduce the result. But it's not the optimal way.
Then, I've tried to rewrite 1 as (2/e)^0, and to solve the equation to find the critical point, but it's still not correct.
Can you help me?
Thanks in advance.
2026-04-11 14:50:38.1775919038
how to solve this exponential inequality?
66 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
The question is answered in the comment but it isn't clear.
Since $2/e$ is less than 1 therefore, if we go with $x>0$ in the comments for any $x$, it would yield a wrong result. For example $(2/e)^{50} = 2.17*10^{-7} \leq 1$
However, for $x < 0$ as a first step, should be a good answer, since the equation will be inversed making it $e/2$ which is number over 1 in the first place.
Start from here.
Continuation
I said start from here, when I gave the full answer without supporting it (proof). Therefore, please rewrite everything in an eloquent way.