Question

solve for x : (viii) logx (8x - 3) - logx 4 = 2.​

Answer 1

Answer:

x₁ = 3 /2

x₂ = 1 /2

Step-by-step explanation:

logₓ (8x - 3) - logₓ 4 = 2.

logₓ (8x - 3) = 2 + logₓ 4

logₓ (8x - 3) = 2logₓ (x) + logₓ 4

logₓ (8x - 3) = logₓ (x)² + logₓ 4

logₓ (8x - 3) = logₓ (x²*4)

8x - 3 = 4x²

- 4x² + 8x - 3 = 0

4x² - 8x + 3 = 0

x = (-b ± √(b² - 4ac)) / 2a

x = (-(-8) ± √((-8)² - 4(4)(3))) / 2(4))

x = (8 ± √(64 - 48)) / 8

x = (8 ± √(16)) / 8

x = (8 ± 4) / 8

x₁ = (8 + 4) / 8 = 12 / 8 = 3 /2

x₂ = (8 - 4) / 8 = 4 / 8 = 1 /2