Let S_n (x)= log_a^1 / 2 x+ log_a^1 / 3 x+ log_a^1 / 6 x+ log_a^1 / 11 x+ log_a^1 / 18 x+ log_a^1 / 27 x+… up to n-terms, where a >1. If S_24(x)=1093…

Let $$\mathrm{S}_{\mathrm{n}}(x)=\log _{\mathrm{a}^{1 / 2}} x+\log _{\mathrm{a}^{1 / 3}} x+\log _{\mathrm{a}^{1 / 6}} x+\log _{\mathrm{a}^{1 / 11}} x+\log _{\mathrm{a}^{1 / 18}} x+\log _{\mathrm{a}^{1 / 27}} x+\ldots \text { up to n-terms, } $$ where $\displaystyle \mathrm{a}>1$. If $\displaystyle \mathrm{S}_{24}(x)=1093$ and $\displaystyle \mathrm{S}_{12}(2 x)=265$, then value of a is equal to \_\_\_\_.