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

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

Simplify

$=\log _{10}\left(\frac{y^3}{x^2z^4}\right)$The final answer$\log _{10}\left(\frac{y^3}{x^2z^4}\right)$