Question

Expand log 12√a*3 b*4c*2 as loga logb logc

Answer 1

The answer is $2log3+2log2+\frac{1}{2}loga+logb+3log2+logc$

Step-by-step explanation:

Given,

Expend $log(12\sqrt{a}\times 3b\times 4c\times 2)$

∴ $log(12\sqrt{a}\times 3b\times 4c\times 2)$

$=log(12\sqrt{a})+log(3b)+log(4c)+log2$

$=log(3\sqrt{16a})+log3+logb+log4+logc+log2$

$=log3+log(16a)^{\frac{1}{2} } +log3+logb+log2^{2} +logc+log2$

$=log3+\frac{1}{2}log(16a)+log3+logb+2log2+logc+log2$

$=log3+\frac{1}{2}(log2^{4}+loga)+log3+logb+2log2+logc+log2$

$=2log3+\frac{1}{2}(4log2+loga)+logb+3log2+logc$

$=2log3+2log2+\frac{1}{2}loga+logb+3log2+logc$

Hence, The answer is $2log3+2log2+\frac{1}{2}loga+logb+3log2+logc$