Question

Write $2\log 3+3\log 5+5\log 2$ as a single logarithm.

Answer 1

$2log3+3log5+5log2$

We know that, ${logx}^y=ylogx$,

Using the above property we can reduce the given equation as,

$={log3}^2+{log5}^3+{log2}^5$

$=log9+log125+log32$

also, $logx+logy+logz=logxyz$, hence we can write the above as,

$=log(9\times 125\times 32)$

$=log\left(36000\right)$

$\therefore$ $2log3+3log5+5log2$ can be written as a single logarithm as $log36000$.