Question

2- Determine o conjunto solução das equações: a) log 4 x = 2 b) log 6 ( x 2 – x ) = 1 c) log 5 ( log 3 x ) = 1 d) log 2 ( 4x + 24 ) = 5 e) log 2 ( 3x + 1 ) = -1

Answer 1

                            Logaritmos

Problema "a" :

$Log_{4} X=2\\\\\\X=2^{4} \\\\\\\boxed{\bf{X=16}}$

Problema "b" :

$Log_{6} (X^{2}-X) =1\\\\\\X^{2} -X=6^{1} \\\\\\X^{2} -X-6=0\\\\\\(X-3)(X+2)=0\\\\X-3=0\\\\\bold{X=3}\\\\\\X+2=0\\\\\bold{X=-2}\\\\\\ \boxed{\bf{C.S={3;-2]}}}$

Problema "c" :

$Log_{5} (Log_{3}X)=1\\\\\\(Log_{3}X)=5^{1} \\\\\\(Log_{3}X)=5\\\\\\X=3^{5} \\\\\\\boxed{\bf{X=243}}$

Problema "d" :

$Log_{2} (4x+24)=5\\\\\\4x+24=2^{5} \\\\\\4x+24=32\\\\\\4x=32-24\\\\\\4x=8\\\\\\\boxed{\bf{X=2}}$

Problema "e" :

$Log_{2} (3x+1)=-1\\\\\\3x+1=2^{-1} \\\\\\3x+1=1/2\\\\\\3x=0,5-1\\\\\\3x=-0,5\\\\\\x=-0,5:3\\\\\\\boxed{\bf{X=\dfrac{-1}{6} }}$