List of top Mathematics Questions on Exponential and Logarithmic Functions asked in UPSEE

If $\log_{\sin \frac{\pi}{6}} \left\{\frac{\left|z-2\right| + 3 }{3\left|z - 2\right| - 1 }\right\}>1 $ , then
Value of $\left[\left(\log_{b}\,a\right)\left(\log_{c}\,b\right)\left(\log_{a}\,c\right)\right]$ is
$\log_3\,2, \log_6\,2, \log_{12}\,2$ are in