Question

Show that $\log 10800=4\log 2+3\log 3+2\log 5$

Answer 1

given that, $\log 10800=\log 16\times 27\times 25$

$=\log 16+\log 27+\log 25$

$=\log 2^4+\log 3^3+\log 5^2$ using $\log \left(ab\right)=\log a+\log b$

$=4\log 2+3\log 3+2\log 5$ using $\log a^m=m\log a$

$=$R.H.S

Hence proved