Question

3 log 3 +2 log 5-2 log 6- log 3

Answer 1

$3 log \: 3 + 2 log \: 5 - 2 log6 - log3 \\ \\ log( {3}^{3} ) + log( {5}^{2} ) - log( {6}^{2} ) - log(3)$


Using property,

$log(m) + log(n) = log(mn)$

and

$log(m) - log(n) = log( \frac{m}{n} )$



Moving in with steps,

$log( {3}^{3} ) + log( {5}^{2} ) - log( {6}^{2} ) - log(3) \\ \\ = log( \frac{ {3}^{3} \times {5}^{2} }{ {6}^{2} \times 3} ) \\ \\ = log( \frac{27 \times 25}{36 \times 3} ) \\ \\ = log( \frac{25}{4} ) \\ \\ = log( \frac{ {5}^{2} }{ {2}^{2} } ) \\ \\ = log({ \frac{5}{2} }^{2}) \\ \\ = 2 log( \frac{5}{2} )$


Hence your answer.

Answer 2

Step-by-step explanation:

log3^3+log5^2-log6^2-log3

=log(27×25÷36÷3)

=log(25/4