Question

what is the solution of Log√(3) 1728
$log_{ \sqrt{3} }(1728)$

Answer 1

So we get =>
$log_{ \sqrt{3} }(1728) = log_{ \sqrt{3} }( {12}^{3} ) = >$
$3 log_{ \sqrt{3} }(12) = 3 log_{ \sqrt{3} }(4)(3) = >$
$3 log_{ \sqrt{3} }(3) + 3 log_{ \sqrt{3} }(4) = >$
$3 log_{ \sqrt{3} }( {( \sqrt{3}}^{2} ) = 6 log_{ \sqrt{3} }( \sqrt{3} ) = 6$
$3 log_{ \sqrt{3} }(4) = 3 \frac{ log(4) }{ log( \sqrt{3} ) } = \frac{ 3 log( {2}^{2} ) }{ log {3}^{0.5} }$
$= > 6 + 6 \frac{ log2}{0.5 log(3) } = 6 + 12 \frac{ log(2)}{ log(3) }$
$= > 6 + 12 \frac{(0.3010)}{(0.4770)} = > 6 + 12(0.631)$
$= > 6 + 7.572 = > 13.572$
13.572 is the answer approximately.