Question

What is the value of logx?y3lodwhen given the following:Zlog(x) = 3log(y)=2log(z)= -1

Answer 1

Given the question

`\log ((x^2y^3)/(z))`

To resolve this, we can follow the steps below

Step1: Apply the logarithm rule

`\log ((x^2y^3)/(z))=\log x^2+\log y^3-\log z`

This will give=>

`\log x^2+\log y^3-\log z=2\log x+3\log y-\log z`

Since we have been given that

`\begin{gathered} \log x=3 \\ \log y=2 \\ \log z=-1 \end{gathered}`

Step2: Substitute the given values into the equation

`2\log x+3\log y-\log z=2(3)+3(2)-(-1)`

=>

`6+6+1=13`

Answer = 13