Verified answer

[tex] log_{4}( \frac{1}{5} ) + log_{4}(36) + \frac{1}{2} log_{4}( \frac{25}{81} ) = \\ log_{4}( \frac{1}{5} ) + log_{4}(36) + log_{4} ( \sqrt{\frac{25}{81} ) } = \\ log_{4}( \frac{1}{5} ) + log_{4}(36) + log_{4}( \frac{5}{9} ) = \\ log_{4}( \frac{36 \times 5}{5 \times 9} ) = log_{4}(4) = 1[/tex]