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# $\lim\limits_{x\to 0}\large\frac{\log x^n-[x]}{[x]}$ $n\in N$ ($x$ denotes greatest integer less than or equal to $x$)

$\begin{array}{1 1}(a)\;has\;value\;-1&(b)\;has\;value\;0\\(c)\;has\;value\;1&(d)\;does\;not\;exist\end{array}$

Since $\lim\limits_{x\to 0}[x]$ does not exist,hence required limit does not exist.
Hence (d) is the correct answer.