Question

Simplify the following expressions.
$(lo{g}_{3}4+lo{g}_{2}9{)}^2-(lo{g}_{3}4-lo{g}_{2}9{)}^2$

Answer 1

$(a+b{)}^2-(a-b{)}^2$

$=(a^2+b^2+2ab)-(a^2+b^2-2ab)$

$=4ab$

Here, we get-

$4.{\log }_{3}4.{\log }_{2}9$

$=\mathrm{4.2.2}{\log }_{3}2.{\log }_{2}3$

$=16$