Question

solve 2log(6/7)+1/2log81/16+log196/27.

Answer 1

$2\ log (\frac{6}{7}) + \frac{1}{2}\ log( \frac{81}{16} )+log( \frac{196}{27}) \\ \\ = log (\frac{6}{7})^2 + log( \frac{81}{16} )^{\frac{1}{2}}+log( \frac{196}{27}) \\ \\ = log (\frac{36}{49}) + log( \frac{9}{4} )+log( \frac{196}{27}) \\ \\ = log( \frac{36}{49} \times \frac{9}{4} \times \frac{196}{27} )\\ \\ = log( \frac{36 \times 9 \times 196}{49 \times 4 \times 27} )\\ \\ =log\ 12$