Question

calcule o valor do logaritmo log625 √5

Answer 1

$log_{625}( \sqrt{5} ) = \frac{ log_{5}( \sqrt{5} ) }{ log_{5}(625) } = \frac{ log_{5}( {5}^{ \frac{1}{2} } ) }{ log_{5}( {5}^{4} ) } = \\ = \frac{ \frac{1}{2} log_{5}(5) }{4 log_{5}(5) } = \frac{ \frac{1}{2} }{4} = \frac{1}{2} \times \frac{1}{4} = \\ \boxed{= \frac{1}{8} = 0.125}$

Answer 2

Logaritmo:

$log_{625}( \sqrt{5} ) = \color{red} {x} \\ {625}^{x} = \sqrt{5} \\ {\diagup\!\!\!\!5}^{4x} = {\diagup\!\!\!\!5}^{ \frac{1}{2} } \\ 4x = \frac{1}{2} \\ x = \frac{1}{2} \div 4 \\ x = \frac{1}{2} \times \frac{1}{4} \\ \boxed{ \bf{x = \frac{1}{8} } }$