Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponents should be positive.
$$4\log \left(x{y}^2\right)+2\log \left(\frac{1}{x}\right)-5\log (y)$$

Step 1 ：Given the expression $4\log \left(x{y}^2\right)+2\log \left(\frac{1}{x}\right)-5\log (y)$

Step 2 ：Apply the properties of logarithms to simplify the expression

Step 3 ：Using the property $\log (a\cdot b)=\log (a)+\log (b)$, the expression $4\log \left(x{y}^2\right)$ can be rewritten as $4\log (x)+8\log (y)$

Step 4 ：Using the property $\log (a/b)=\log (a)-\log (b)$, the expression $2\log \left(\frac{1}{x}\right)$ can be rewritten as $2\log (1)-2\log (x)$

Step 5 ：Combine the above steps, the expression becomes $4\log (x)+8\log (y)+2-2\log (x)-5\log (y)$

Step 6 ：Simplify the expression by combining like terms, the expression becomes $2\log (x)+3\log (y)$

Step 7 ：Final Answer: The final simplified expression is $\boxed{{\displaystyle 2\log (x)+3\log (y)}}$