Chapter 9.4, Problem 87ES

(a)

To determine

To calculate: The expanded form of the expression ${\log }_a\frac{\sqrt{x^{4}y}}{\sqrt{x{y}^3}}$ where $x>0$ and $y>0$ using quotient rule.

(b)

To determine

To calculate: The expand form of the expression ${\log }_a\frac{\sqrt{x^{4}y}}{\sqrt{x{y}^3}}$ where $x>0$ and $y>0$ using product rule.

(c)

To determine

The simplified form of the expression $\frac{\sqrt{x^{4}y}}{\sqrt{x{y}^3}}$ and then find expanded form of ${\log }_a\frac{\sqrt{x^{4}y}}{\sqrt{x{y}^3}}$ where $x>0$ and $y>0$.

(d)

To determine

Whether all answers from the above three parts are correct and the expression $\frac{\sqrt{x^{4}y}}{\sqrt{x{y}^3}}$ can be simplified by all three methods.