Question

Prove that log(75/16)-2log(5/9)+log(32/243)

Answer 1

We have to simplify $\log(75/16)-2\log(5/9)+\log(32/243)$.

Make use of the identities,

$\log a+\log b= \log ab\\ m\log a=\log a^m$

$\log(75/16)-2\log(5/9)+\log(32/243)=\log(75/16)-\log(25/81)+\log(32/243)\\ =\log(75/16)+\log(32*81/243*25)\\ =\log(75/16)+\log(32/75)\\ =\log(75*32/16*75)\\ =\log (2)$