Question

$\large \mathtt{log_{3 \sqrt{3} }(243)}$
Evaluate the following:​

Answer 1

$\underline{\huge{Answer:-}}$

Step-by-step explanation:

$\implies \large \mathbb{ log_{3 \sqrt{3} }(243) = \frac{ log(243) }{ log(( 3\sqrt{3} ) } }$

$\implies \: = \large \mathbb{ \frac{ log( {3}^{5} ) }{ log(3 \times {3}^{ \frac{1}{2} } ) } = \frac{ log( {3}^{5} ) }{ log( {3}^{ 1 + \frac{1}{2} } ) } }$

$\implies \: = \large \mathbb{ \frac{ log( {3}^{5} ) }{ log( {3}^{ \frac{3}{2} } ) } = \frac{5 log(3) }{ \frac{3}{2} log(3) } }$

$\implies \: = \large \mathbb{ \frac{5}{ 3/2} }$

$\implies \: = \large \fbox\mathcal{ \frac{10}{3} }$