Resumen - Soluciones

\[\log_{5}(5^{-5}) = \boxed{-5}\]

\[\log_{4}(4^{-1}) = \boxed{-1}\]

\[\log_{9} (81) = \log_9\left(9^\boxed{{2}}\right) = \boxed{2}\]

\[\log_{11} (1) = \log_{11} (11^0) = \boxed{0}\]

\[\log_{11} (1) = \boxed{0}\]

\[\log_{2} (2^{x}) = \boxed{x}\]

\[\log_{5} (5^{x^{8}*9}) = \boxed{9x^{8}}\]

\[\log_{5} (5^{x^{8}}*25) = \boxed{(x^{8}+2)}\]

\[\log_{9} (9^{x^{9}}*9*9) = \boxed{x^{9}+2}\]

\[\log_{9} (9^{x^{7}}*9*9) = \boxed{x^{7}+2}\]

\[\log_{10} (10^{4x^{7}}*10^{x+2})) = \boxed{4x^{7}+x+2}\]

\[\log_{4} (4^{5x^{4}}*4^{x+2})) = \boxed{5x^{4}+x+2}\]