Question

Resolva as equações logarítmicas a seguir:

1) log3(2x + 9) = log3(-x + 12)

2) loga(8x + 4) = loga (6x + 10)

3) log3(x² - 6x+ 4) = 2

4) log5(x² - 3x + 27) = 2

Answer 1

1) log3(2x + 9) = log3(-x + 12)

2x = 12 - x - 9

2x = 3 - x

2x + x = 3

3x = 3

x = 1

2) loga(8x + 4) = loga (6x + 10)

8x = 6x + 10 - 4

8x = 6x + 6

8x - 6x = 6

2x = 6

x = 6/2

x = 3

3) log3(x² - 6x+ 4) = 2

x²-6x+4=3²

x²-6x+4=9

x²-6x-5=0

x = 6+2⎷14/2 , 6-2⎷14/2

x = 3+⎷14, 3-⎷14

4) log5(x² - 3x + 27) = 2

x² - 3x + 27 = 5²

x² - 3x + 27 = 25

x² - 3x + 2 = 0

(x-2)(x-1)=0

x = 2,1