Question

Expand a logarithmic expression.

Answer 1

we are given

$log(z^3\sqrt{x^5y} )$

step-1: Firstly , we will expand log terms by using property

$log(a*b)=log(a)+log(b)$

$log(z^3)+log(\sqrt{x^5y} )$

step-2: Now, we can bring exponent in front

$log(a^n)=n*log(a)$

$=log(z^3)+log(x^5y)^{\frac{1}{2}}$

$=3log(z)+\frac{1}{2}log(x^5y)$

step-3: we can again expand second term

$=3log(z)+\frac{1}{2}(log(x^5)+log(y))$

$=3log(z)+\frac{1}{2}(5log(x)+log(y))$

so, we will get

$=3log(z)+\frac{1}{2}(5log(x)+log(y))$...............Answer