Question

Find the value of log 243 to the base 3root 3

Answer 1

Answer:

$\huge\bold\red{\frac{10}{3}}$

Explanation:

$log_{3 \sqrt{3} }(243) \\ \\ = log_{ ({3}^{1} \times {3}^{ \frac{1}{2} } ) }( {3}^{5} ) \\ \\ = log_{ {3}^{(1 + \frac{1}{2}) } }( {3}^{5} ) \\ \\ = log_{ {3}^{ \frac{3}{2} } }( {3}^{5} ) \\ \\ = 5 \times \frac{2}{3} \times log_{3}(3) \\ \\ = \frac{10}{3}$

Concept used :-

$1. \: log_{a}(a) = 1 \\ \\ 2. \: log_{ {a}^{n} }( {b}^{m} ) = \frac{m}{n} \times log_{a}(b)$