Question

find the value of log 9√3 to the base of 1÷3
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Answer 1

The principle applied here is

$log_{m}( {m}^{n} ) = n$

Now coming to the question,

$log_{ \frac{1}{ 3} }(9 \sqrt{3} ) \\ = log_{ \frac{1}{3} }(9) + log_{ \frac{1}{3} }( \sqrt{3} ) \\ = log_{ \frac{1}{3} }( { \frac{1}{3} })^{ - 2} + log_{ \frac{1}{3} }( { \frac{1}{3} })^{ - \frac{1}{2} } \\ = - 2 - \frac{1}{2} \\ = - \frac{5}{2}$

HOPE IT HELPS!!