Question

log243 tothe base root 3​

Answer 1

Answer:-

10

Explanation:-

$log_{ \sqrt{3} }(243) \\ \\ = log_{ {3}^{\frac{1}{2} } }( {3}^{5} ) \\ \\ = \frac{5}{ \frac{1}{2} } log_{3}(3) \: \: \: ( log_{ {b}^{n} }( {a}^{m}) = \frac{m}{n} log_{b}(a) ) \\ \\ = 10 \: log_{3}(3) \\ \\ = 10(1) \: \: ( log_{a}(a) = 1)\\ \\ = 10$