Verified answer

[tex]38 {}^{ log_{3.8}(11) } = 11 \\ 3 {}^{2 - log_{3}(18) } = 3 {}^{2} \times 3 {}^{ - log_{3}(18) } = 9 \times 3 {}^{ log_{3}(18 {}^{ - 1} ) } = 9 \times \frac{1}{18} = 0.5 \\ 6 {}^{ - 2 log_{6}(5) } = 6 {}^{ log_{6}(5 {}^{ - 2} ) } = 5 {}^{ - 2} = \frac{1}{25} = 0.04 \\ log_{2}(7) - log_{2}( \frac{7}{16} ) = log_{2}(7 \div \frac{7}{16} ) = log_{2}(16) = 4 \\ log_{10}(13) - log_{10}(130) = log_{10}(13 \div 130) = log_{10}( \frac{1}{10} ) = - 1 \\ log_{10}(8) + 3 \times log_{10}(5) = log_{10}(8) + log_{10}(5 {}^{3} ) = log_{10}(8) + log_{10}(125) = log_{10}(8 \times 125) = log_{10}(1000) = 3[/tex]