Question

express in terms of log 2 and log 3 : (1÷2 log 54 × 1÷3 log 243)

Answer 1

$\frac{1}{2 log(54) } \times \frac{1}{3 log(243) } \\ = \frac{1}{2 log(2 \times {3}^{3} ) } \times \frac{1}{3 log( {3}^{5} ) } \\ = \frac{1}{ 2( log(2) + log( {3}^{3} ) ) } \times \frac{1}{15 log(3) } \\ = \frac{1}{2( log(2) + 3 log(3) ) } \times \frac{1}{15 log(3) }$