Question

Resolva as equações logarítmicas a seguir:

Answer 1

a) log ₂ 7x - 3 = 4
7x - 3 = 2⁴
7x - 3 = 16
7x = 16 + 3
7x = 19
x = 19/7

b) log ₂ x² - 2x = 3
x² - 2x = 2³
x² - 2x = 8
x² - 2x - 8 = 0

Δ = b² -4ac                    x = -b+/-√Δ/2a
Δ = (-2)² - 4.(1).(-8)       x = 2 +/-6/2
Δ = 4 + 32                     x' = 4
Δ = 36                           x'' = -2

c) log ₃ 4x-1/3 = -2
4x - 1/3 = 3⁻²
4x - 1/3 = 1/9
9.(4x-1) = 3
36x - 9 = 3
36x = 3 + 9
36x = 12
x = 12/36
x = 1/3

d) log ₓ x² - 6x + 7 = 2
x² - 6x + 7 = x²
x² - x² - 6x + 7 = 0
-6x + 7 = 0
-6x = -7
x = 7/6

e) log ₃ x² - 4x + 9 = 2
x² - 4x + 9 = 3²
x² - 4x + 9 = 9
x² - 4x = 9 - 9
x² - 4x = 0

x (x - 4) = 0
x = 0 ou...

x-4 = 0
x = 4