Properties of Log-Sums

Algebra Level 3

Let

$A= \sum_{n=1}^{2014}{n} ~~~\text{and} ~~~ B= \sum_{n=1}^{2014}{n^3}.$

Find the value of $$\log_{\sqrt A} {B}$$

Note: This question is taken from NTSE (Tamil Nadu) 2014.

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