how would one solve the following equation

Question

How could the following equation be solved?

$$ 100x^2=2^x $$

This is as far as I have got: $$ \ln(100x^2) = \ln(2^x) $$

Answer 1

This equation cannot be solved in terms of simple functions. You will need the Lambert W function.

The equation has multiple solutions, one of which is $$x = -2 \,\frac{ W(\ln(2)/20)}{\ln(2)} \approx 0.103658.$$