# Chapter 4 - Review - Exercises: 53

$$\log_2 (\frac{ (x-y)^{\frac{3}{2}}}{(x^2 + y^2)^2})$$

#### Work Step by Step

$Combine$ $into$ $a$ $single$ $logarithm:$ $\frac{3}{2}\log_2 (x-y)$ - $2\log_2 (x^2+y^2)$ Use the Third Law of Logarithms for both portions $\frac{3}{2}\log_2 (x-y)$ = $\log_2 (x-y)^{\frac{3}{2}}$ $2\log_2 (x^2 + y^2)$ = $\log_2 (x^2 + y^2)^2$ $\log_2 (x-y)^{\frac{3}{2}}$ - $\log_2 (x^2 + y^2)^2$ Use the Second Law of Logarithms $\log_2 (x-y)^{\frac{3}{2}}$ - $\log_2 (x^2 + y^2)^2$ = $\log_2 (\frac{ (x-y)^{\frac{3}{2}}}{(x^2 + y^2)^2})$ $$\log_2 (\frac{ (x-y)^{\frac{3}{2}}}{(x^2 + y^2)^2})$$

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