Question

Resolva as seguintes equações:
a) log4(x+3) = 1
b) log4(x – 3) = log4(-x+ 7)
c) log5 (2x + 3) = log5 x
d) log3 (log6 x) = 0​

Answer 1

a)

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

b)

$log_{4}(x - 3) = log_{4}( - x + 7) \\ x - 3 = - x + 7 \\ x + x = 7 + 3 \\ 2x = 10 \\ x = \frac{10}{2} \\ x = 5$

c)

$log_{5}(2x + 3) = log_{5} \: x \\ 2x + 3 = x \\ 3 = x - 2x \\ 3 = - x \\ x = - 3$

d)

$log_{3}( log_{6} \: x ) = 0 \\ {3}^{0} = log_{6} \: x \\ log_{6} \: x = 1 \\ {6}^{1} = x \\ x = 6$