Question

determine o conjunto verdade das seguintes eqaçoes logaritimicas:a)log2(xmenos1)mais log(xmenos2)igual a 1.

B)log x base3 mais logbase9 x igual a 3

Answer 1

$a) log_{2} (x-1) + log_{2} (x-2) = 1 => log_{2} [(x-1).(x-2)] = 1 => (x-1).(x-2)=2^{1} => x^{2}-3x+2 = 2=> x^{2}-3x = 0$

$b) log_{3} x +log_{9} x = 3 =>log_{3} x +log_{(3.3)} x = 3 => log_{3} x +[log_{3} x/ log_{3} (3.3)] = 3 => log_{3} x +[log_{3} x/ log_{3} 3 +log_{3}3 ] = 3 => log_{3} x +log_{3} x/ 2 = 3 => 3.log_{3} x/2 = 3 => 3.log_{3} x = 6 => log_{3} x^{3} = 6 =>x^{3} =3^{6} =>  x^{3} =729 => x =\sqrt[3]{729} => x = 9$