Answer
$\log 4 + 3\log x - 2\log y + 5\log (x-1)$
Work Step by Step
$Expand$ $the$ $logarithmic$ $expression:$
$\log (\frac{4x^3}{y^2(x-1)^5})$
Use the Second Law of Logarithms
$\log (\frac{4x^3}{y^2(x-1)^5}) = \log 4x^3 - \log y^2(x-1)^5$
Use the First Law of Logarithms for $\log 4x^3$ and $\log y^2(x-1)^5$
$\log (4\times x^3) = \log 4 + \log x^3$
$\log (y^2(x-1)^5) = \log y^2 + \log (x-1)^5$
$\log 4x^3 - \log y^2 + \log (x-1)^5$
Use the Third Law of Logarithms for the whole expression
$\log 4 + \log x^3 - \log y^2 + \log (x-1)^5 = \log 4 + 3\log x - 2\log y + 5\log (x-1)$