Question

What is 3log y-2 log x-4 log z written as a single logarithm?

Answer 1

Given

`3logy-2logx-4logz`

Solution

`3\log _(10)\left(y\right)-2\log _(10)\left(x\right)-4\log _(10)\left(z\right)`

Apply log rule

`\begin{gathered} =\log _(10)\left((y^3)/(x^2)\right)-\log _(10)\left(z^4\right) \\ \\ \\ =\log _(10)\left(((y^3)/(x^2))/(z^4)\right) \\ \end{gathered}`

Simplify

`=\log _(10)\left((y^3)/(x^2z^4)\right)`The final answer
`\log _(10)\left((y^3)/(x^2z^4)\right)`