Question

Ache o valor de x da equação 400^x=1/200

Answer 1

Resposta:

${400}^{x} = \frac{1}{200} \\ log_{400}( \frac{1}{200} ) = x \\ x = log_{400}(1) - log_{400}(200) \\ x = 0 - log_{400}(200) \\ x = - log_{400}(200) \\ x = - log_{400}( {10}^{2} \times 2 ) \\ x = - (log_{400}( {10}^{2} ) + log_{400}(2) ) \\ x = - (2 log_{400}(10) + log_{400}(2) ) \\ \boxed{\boxed{x = - 2 log_{400}(10) - log_{400}(2)}}$