Explicação passo-a-passo:

[tex]s)[/tex]

[tex] log_{7}( \sqrt{ \frac{1}{49} } ) = x[/tex]

[tex] {7}^{x} = \sqrt{ \frac{1}{49} } [/tex]

[tex] {7}^{x} = \frac{1}{7} [/tex]

[tex] {7}^{x} = {7}^{ - 1} [/tex]

[tex]x = - 1[/tex]

[tex]t)[/tex]

[tex] log_{3}( \sqrt{ \frac{1}{9} } ) = x[/tex]

[tex] {3}^{x} = \sqrt{ \frac{1}{9} } [/tex]

[tex] {3}^{x} = \frac{1}{3} [/tex]

[tex] {3}^{x} = {3}^{ - 1} [/tex]

[tex]x = - 1[/tex]

[tex]u)[/tex]

[tex] log_{ \frac{3}{2} }( \frac{4}{9} ) = x[/tex]

[tex]( { \frac{3}{2}) }^{x} = \frac{4}{9} [/tex]

[tex]( { \frac{3}{2} )}^{x} = ( { \frac{2}{3}) }^{2} [/tex]

[tex]( { \frac{3}{2} )}^{x} = ( { \frac{3}{2} )}^{ - 2} [/tex]

[tex] \: \: \: \: x = - 2[/tex]

[tex]v)[/tex]

[tex] log_{ 3}( \frac{1}{243} ) = x[/tex]

[tex] {3}^{x} = \frac{1}{243} [/tex]

[tex] {3}^{x} = \frac{1}{ {3}^{5} } [/tex]

[tex] {3}^{x} = {3}^{ - 5} [/tex]

[tex]x = - 5[/tex]