Question

Log4(x-3)+log16(x-3)=3

Answer 1

Resposta:

$x = 19$

Explicação passo-a-passo:

$log_{4}( x - 3) + log_{16}(x - 3) = 3$

$log_{4}(x - 3) + log_{16}(x - 3) = 3,x > 3$

$log_{4}(x - 3) + log_{ {4}^{2} }(x - 3) = 3$

$log_{4}(x - 3) + \frac{1}{2} \times log_{4}(x - 3) = 3$

$log_{4}(x - 3) + log_{4}((x - 3) ^{ \frac{1}{2} } ) = 3$

$log_{4}((x - 3) \times {(x - 3)}^{ \frac{1}{2} } ) = 3$

$log_{4}( {(x - 3)}^{ \frac{3}{2} } ) = 3$

${(x - 3)}^{ \frac{3}{2} } = {4}^{3}$

${(x - 3)}^{ \frac{3}{2} } = 64$

${ {((x - 3)}^{ \frac{3}{2} }) }^{ \frac{2}{3} } = {64}^{ \frac{2}{3} }$

$x - 3 = {64}^{ \frac{2}{3} }$

$x - 3 = { {(2}^{6} )}^{ \frac{2}{3} }$

$x - 3 = {2}^{4}$

$x - 3 = 16$

$x = 16 + 3$

$x = 19,x > 3$

$x = 19$