Question

log4(x-3) -log16(x-3)=1

Answer 1

$log_{4}(x - 3) - log_{16}(x - 3) = 1$

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

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

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

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

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

$\sqrt{x - 3} = 4$

$x - 3 = 16$

$x = 16 + 3$

$x = 19$