Explanation:
The intermediate value theorem (IVT) tells you that for continuous function ...
f(x) = 11^x
if f(1) < 12 and f(2) > 12, then for f(x) = 12, the value of x must be between 1 and 2.
We know f(1) = 11^1 = 11 < 12, and f(2) = 11^2 = 121 > 12, so the conditions are met for the IVT to be applicable.
__
In short, the Intermediate Value Theorem says so.
