1) yes, BUT: it's not "prove it is non-integer" but rather irrational. Therefore the equation is 10^x=15^y
2) Simplify them by considering the number of 2's multiplied together on LHS, then RHS, and repeat.
eg in 5! there are 3 powers of 2, 20! there are 18, so 21 on LHS. RHS: similarly you...