Question

Show that $\log 360=3\log 2+2\log 3+\log 5$

Answer 1

$\log 360=\log \left(3^2{.2}^3.5\right)$

$=\log 3^2+\log 2^3+\log 5\dots (\log a+\log b+\log c=\log (abc\left)\right)$

$\log 360=3\log 2+2\log 3+\log 5.\dots (\because n{\log }_{a}b={\log }_a{b}^n)$

Hence, proved