Question

4) Resolva as equações logarítmicas:

Answer 1

Explicação passo-a-passo:

a)

Igualando os logaritmandos:

8x - 5 = 5x + 7

8x - 5x = 7 + 5

3x = 12

x = 12/3

x = 4

b)

Igualando os logaritmandos;

y³ + 3 = 32

y³ = 32 - 3

y³ = 29

y = ∛29

c)

log(1/2) (6x - 4) = -5

6x - 4 = (1/2)^(-5)

6x - 4 = 2⁵

6x - 4 = 32

6x = 32 + 4

6x = 36

x = 36/6

x = 6

d)

log3 (5x + 1) = 4

5x + 1 = 3⁴

5x + 1 = 81

5x = 81 - 1

5x = 80

x = 80/5

x = 16

e)

log5 (7x + 6) = 3

7x + 6 = 5³

7x + 6 = 125

7x = 125 - 6

7x = 119

x = 119/7

x = 17