Question

PROVE THAT :

2log15/18 - log25/162 + log4/9 = log2

Answer 1

Hey!!

Solution→Refer to the attachment...

Answer 2

SOLUTION:-

L.H.S

$2log( \frac{15}{18} ) - log( \frac{25}{162} ) + log( \frac{4}{9} ) \\ \\ = > 2log( \frac{5}{6} ) - log25 + log162 + log4 - log9 \\ \\ = > 2log5 - 2log6 - log {5}^{2} + log(2 \times {3}^{4} ) + log {2}^{2} - log {3}^{2} \\ \\ = > 2log5 - 2log(2 \times 3) - 2log5 + log2 + 4log3 + 2log2 - 2log3 \\ \\ = > 2log5 - 2log2 - 2log 3 - 2log5 + log2 + 4log3 + 2log2 - 2log3 \\ \\ = > 2log5 - 2log5 + 4log3 - 4log3 + ( - 2log2 + 2log2 + log2) \\ \\ = > log \: 2$

R.H.S

Hope it helps ☺️