Question

GENTE PRECISO MUITO DE AJUDA, pfvrrrrrrr

Answer 1

Resposta:

A, C, D, B

Explicação passo-a-passo:

A =

$log_{25}(0.2) = log_{25}( \frac{2}{10} ) = \\ \frac{ log( \frac{2}{10} ) }{ log(25) } = \frac{ log( \frac{1}{5} ) }{ log( {5}^{2}) } = \frac{ log( {5}^{ - 1} ) }{2 log(5) } = \frac{ - 1 log(5) }{2 log(5) } = \frac{ - 1}{2}$

B =

$log_{7}( \frac{1}{49} ) = \frac{ log( \frac{1}{49} ) }{ log(7) } = \frac{ log( \frac{1}{ {7}^{2} } ) }{ log(7) } = \frac{2 log(7) }{ log(7) } = 2$

C =

$log_{0.25}( \sqrt{8} ) = log_{ \frac{1}{4} }( {8}^{ \frac{1}{2} } ) = \\ \frac{ log( {8}^{ \frac{1}{2} } ) }{ log( \frac{1}{4} ) } = \frac{ \frac{1}{2} log(8) }{ log( {4}^{ - 1} ) } = \frac{ \frac{1}{2} log( {2}^{3} ) }{ log( {2}^{2} ) } = \frac{ \frac{1}{2} \times 3 log(2) }{2 log(2) } = \frac{ \frac{3}{2} }{2} = \frac{3}{4}$

D =

$log(0.1) = log( \frac{1}{10} ) = log( {10}^{ - 1} ) = - 1 log(10) = - 1$

Ordem crescente:

-1/2, 3/4, 1, 2