If the third term in the binomial expansion of $$1+xlog2$$⁡$$x5equals$$ $$2560$$, then a possible value of x is

Question

If the third term in the binomial expansion of $$1+xlog2$$⁡$$x5equals$$ $$2560$$, then a possible value of x is

Infinity Learn · Accepted Answer

The (r$$ $$+$$ $$1)th$$ term in the expansion of $$(a$$ $$+$$ $$x)n$$ is Given by  $$Tr+1=nCran$$−rxr.'. $$3rd$$ term in the expansion of $$1+xlog2$$⁡$$x5$$ is  $$5C2(1)5$$−$$2xlog2$$⁡$$x2$$⇒ $$5C2(1)5$$−$$2xlog2$$⁡$$x2$$⇒ $$2560$$⇒ $$10xlog2$$⁡$$x2=2560$$⇒  $$x2log2$$⁡$$x=256$$⇒ $$log2$$⁡$$x2log2$$⁡$$x=log2$$⁡$$256$$       $$(given) (taking$$ $$Log2$$ on both $$sides) ⇒$$2log2$$⁡$$xlog2$$⁡$$x=8$$ ∵$$log2$$⁡$$256=log2$$⁡$$28=8log2$$⁡$$x2=4$$⇒$$log2$$⁡$$x=$$±$$2$$⇒$$log2$$⁡$$x=2$$ or $$log2$$⁡$$x=$$−$$2$$⇒$$x=4$$ or $$x=2$$−$$2=14$$

If the third term in the binomial expansion of ${(1 + x^{\log_{2} x})}^{5}$ equals 2560, then a possible value of x is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the third term in the binomial expansion of 1+xlog2⁡x5equals 2560, then a possible value of x is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the third term in the binomial expansion of ${(1 + x^{\log_{2} x})}^{5}$ equals 2560, then a possible value of x is