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If the fourth term in the binomial expansion of $\left(\frac{1}{\sqrt[x]{1+\log_{10} x}} + x^{1/12}\right)^6$ is equal to 200, and $x > 1$, then the value of $x$ is:
(1) 100 (2) 10 (3) $10^3$ (4) $10^4$
Let $t = \log_{10} x$. Solving $t^2 + 4t - t - 4 = 0$: $t = 1$, $x = 10$.
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