If the fourth term in the binomial expansion of $$x11+log10$$⁡$$x+x1126$$ is equal to $$200$$, and x$$1$$ then the value of x is

Question

If the fourth term in the binomial expansion of $$x11+log10$$⁡$$x+x1126$$ is equal to $$200$$, and x>$$1$$ then the value of x is

Infinity Learn · Accepted Answer

Given binomial is $$x11+log10$$⁡$$x+x1126Since$$, the fourth term in the given expansion is $$200$$∴  $$6C3x11+log10$$⁡$$x32x1123=200$$⇒  $$20$$×$$x321+log10$$⁡$$x+14=200$$⇒  $$x321+log10$$⁡$$x+14=10$$⇒ $$321+log10$$⁡$$x+14log10$$⁡$$x=1$$[applying $$log10$$ both sides]⇒  $$6+1+log10$$⁡$$xlog10$$⁡$$x=41+log10$$⁡x⇒  $$7+log10$$⁡$$xlog10$$⁡$$x=4+4log10$$⁡x⇒ $$t2+7t=4+4t$$  $$t2+3t$$−$$4=0$$⇒  $$t=1$$,−$$4=log10$$⁡x⇒$$x=10$$,$$10$$−$$4$$⇒ x>$$1$$ Since, , $$x=10$$

If the fourth term in the binomial expansion of ${(\sqrt{x^{(\frac{1}{1 + \log_{10} x})}} + x^{\frac{1}{12}})}^{6}$ is equal to 200, and $x > 1$ then the value of x is

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If the fourth term in the binomial expansion of x11+log10⁡x+x1126 is equal to 200, and x>1 then the value of x is

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If the fourth term in the binomial expansion of ${(\sqrt{x^{(\frac{1}{1 + \log_{10} x})}} + x^{\frac{1}{12}})}^{6}$ is equal to 200, and $x > 1$ then the value of x is