An algebra problem by Vikram Singh

For each real number x, let $\lfloor x \rfloor$ denote the greatest integer that does not exceed x.

For how many positive integers n is it true that meet two conditions.

(a) $200 \leq x \leq 300$

(b) $\lfloor \log_{2}{x}\rfloor$ = $\lfloor \log_{3}{x}\rfloor$ + $\lfloor \log_{4}{x}\rfloor$