Math Olympiad Question | Lambert W Function | 27^(x) = 1/x

In this Math video, we shall solve an exponential equation 27^(x) = 1/x using the Lambert W function. This question was taken from Mathematics Olympiad.

[marklevin]

27^х is always a positive number. Therefore if solutions exist 1/x must be positive, therefore x is positive. For positive x 27^x is an increasing function and 1/x is decreasing. Therefore these two functions can have equal values at at most one point. Now it is not ha red d to guess which one.

[tomasbabelis]

overcomplicating things on a whole new level...