Question

2) Calcule o valor de x:
a) Log2x = 7
b) Log (1/3)x = 2
c) Log x27 = 3
d) Log x125/8 = 3
e) Log 1/39 = X
f) Log 1/432 = X
g) Log 2V8 = X
h) Log (5/2)x = -1​

Answer 1

a) log₂x = 7

2⁷ = x

x = 128

b) log₁/₃ x = 2

(1/3)² = x

x = 1/9

c) logₓ 27 = 3

x³ = 27

x³ = 3³

x = 3

d) log ₓ 125/8 = 3

x³ = 125/8

x³ = 5³/2³

x³ = (5/2)³

x = 5/2

e) log ₃ 1/9 = x

3ˣ = 1/9

3ˣ = 9⁻¹

3ˣ = 3⁻²

x = -2

f) log ₄ 1/32 = x

4ˣ = 1/32

2²ˣ = 32⁻¹

2²ˣ = 2⁻⁵

2x = -5

x = -5/2

g) log ₂ √8 = x

2ˣ = √8

2ˣ = √(2 . 4)

2ˣ = 2√(2)

2ˣ = 2¹ . 2⁰,⁵

2ˣ = 2¹,⁵

x = 1,5

h) log ₅/₂ x = -1

(5/2)⁻¹ = x

2/5 = x

x = 2/5