If the fourth term in the binomial expansion of + æ ö ç ÷ + è ø 10 6 1 12 1 log 1 x x x is equal to 200, and x > 1, then the value of x is:

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