Question

Calculati:$(log_{3} 36) *( log_{\sqrt{6} } 3 )-(log_{5}8)*(log_{2\sqrt{2} }5 )$

Answer 1

$log_{3}(36) \times log_{ \sqrt{6} }(3) - log_{5}(8) \times log_{2 \sqrt{2} }(5)$

$= log_{3}( ({ \sqrt{6}) }^{4} ) \times \frac{1}{ log_{3}( \sqrt{6} ) } - log_{5}( {(2 \sqrt{2}) }^{2} ) \times \frac{1}{ log_{5 }(2\sqrt2) }$

$= \frac{4 log_{3}( \sqrt{6} ) }{ log_{3}( \sqrt{6} ) } - \frac{2 log_{5}(2 \sqrt{2} ) }{ log_{5}(2 \sqrt{2} ) } = 4 - 2 = 2$