Question

please solve this question friends please please

Answer 1

Final Answer : log3
Steps:
1)
$5 log_{4 \sqrt{2} }(3 - \sqrt{6} ) - \\ 6 log_{8}( \sqrt{3} - \sqrt{2} ) \\ = 5 log_{ {2}^{ \frac{5}{2} } }( \sqrt{3}( \sqrt{3} - \sqrt{2} ) ) - \\ 6 log_{ {2}^{3} }( \sqrt{3} - \sqrt{2} ) \\ = 5 \times \frac{2}{5} (log_{2}( \sqrt{3} ) + \\ log_{2}( \sqrt{3} - \sqrt{2} ) ) - \\ 6 \times \frac{1}{3} log_{2}( \sqrt{3} - \sqrt{2} ) \\ = 2 log_{2}( \sqrt{3} ) + 2 log_{2}( \sqrt{3} - \sqrt{2} ) \\ - 2 log_{2}( \sqrt{3} - \sqrt{2} ) \\ = log_{2}(3)$