Question

resolva as equações :
a)log2^(x-1) + log 2^(x-3) = 3 
b)log2^(x+5) - log 2^(x-1) = 3

Answer 1

a)
$\log_2{(x-1)(x-3)=3$

$(x-1)(x-3)=2^3$

$x^2-4x-3=8$

$x^{2} -4x-5=0$

$x= \frac{-b\pm \sqrt{b^2-4ac} }{2a} = \frac{4\pm \sqrt{16+20} }{2} =$

$x= \frac{4\pm6}{2}$

$x'= \frac{4+6}{2} = \frac{10}{2} =5$

$x"= \frac{4-6}{2} =- \frac{2}{2} =-1$

S={-1,5}

b)
$\log_2{( \frac{x+5)}{(x-1)} =3$

$\frac{x+5}{x-1} =2^3$

$\frac{x+5}{x-1} =8$

$8(x-1)=x+5$

$8x-8=x+5$

$8x-x=5+8$

$7x=13$

$x= \frac{13}{7}$