Question

Expand a logarithmic expression.

Answer 1

we are given

`log(z^3√(x^5y) )`

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

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

`log(z^3)+log(√(x^5y) )`

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

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

`=log(z^3)+log(x^5y)^{(1)/(2)}`

`=3log(z)+(1)/(2)log(x^5y)`

step-3: we can again expand second term

`=3log(z)+(1)/(2)(log(x^5)+log(y))`

`=3log(z)+(1)/(2)(5log(x)+log(y))`

so, we will get

`=3log(z)+(1)/(2)(5log(x)+log(y))`...............Answer