/sci/ - Science & Math

Scientifically speaking, why do I find the idea of getting a deranged and broken girlfriend fascinating?

>>12773831
No problem! Recall that for all [math] x, y > 0, y^{\log_y(x)} = x. [/math] Then, using your expression for the argument of the exponential, we see that this limit simplifies to [eqn]\lim_{x \to \infty} \frac{\log_{10}(x)^{\frac{1}{\log_2(10)}} \log_{10}(x)^{\frac{1}{2}} }{x}. [/eqn] From here you should be able to make an argument using L'hopital's rule that the limit goes to 0. I might recommend comparing it to a similar limit, but which has an integer power of the logs in the numerator to make things a bit easier for your notation and math.