Write the following as a sum of logarithms:
\[
\ln \left(\frac{e^{3} x^{4}}{y^{5}}\right)=\square+\square \ln (x)+\square \ln (y)
\]

Step 1 ：Write the following as a sum of logarithms: \(\ln \left(\frac{e^{3} x^{4}}{y^{5}}\right)=\square+\square \ln (x)+\square \ln (y)\)

Step 2 ：The question is asking to express the given logarithmic expression as a sum of logarithms. The properties of logarithms can be used to simplify the expression. The properties of logarithms that will be used are:

Step 3 ：1. The logarithm of a quotient is the difference of the logarithms: \(\ln(a/b) = \ln(a) - \ln(b)\)

Step 4 ：2. The logarithm of a product is the sum of the logarithms: \(\ln(ab) = \ln(a) + \ln(b)\)

Step 5 ：3. The logarithm of a power is the product of the logarithm and the exponent: \(\ln(a^n) = n\ln(a)\)

Step 6 ：Using these properties, the given expression can be simplified as follows: \(\ln \left(\frac{e^{3} x^{4}}{y^{5}}\right) = \ln(e^3) + \ln(x^4) - \ln(y^5)\)

Step 7 ：Then, applying the third property of logarithms: \(\ln(e^3) + \ln(x^4) - \ln(y^5) = 3\ln(e) + 4\ln(x) - 5\ln(y)\)

Step 8 ：Since the natural logarithm of e is 1, the final expression is: \(3\ln(e) + 4\ln(x) - 5\ln(y) = 3 + 4\ln(x) - 5\ln(y)\)

Step 9 ：Final Answer: \(\ln \left(\frac{e^{3} x^{4}}{y^{5}}\right) = \boxed{3 + 4\ln(x) - 5\ln(y)}\)