Answer
See below
Work Step by Step
$$\frac{1}{4}\log_5 81-\frac{1}{4}\log_5 4\\=\log_581^{\frac{1}{4}}-\log_54^{\frac{1}{4}}\\=\log_5(\frac{81^{\frac{1}{4}}}{4^{\frac{1}{4}}})\\=\log_5 \frac{3}{\sqrt 2}\\=\log_5 (\frac{3\sqrt 2}{2})$$
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