Newton's Nightmares

Algebra Level 5

Determine for what value of $$x$$ is the difference between $$9$$ times the third term of binomial expansion of $$\left( \frac{\sqrt{2^{x-1}}}{\sqrt[3]{2}}+\sqrt[3]{4}\cdot 2^{\frac{x}{2}}\right) ^m$$ and the fifth term of the same expansion equal to $$240$$, if it is known, that the difference between the log of the tripled binomial coefficient of the fourth term of expansion and the log of the binomial coefficient of the second term is equal to $$1$$.

×