Question

Identify a solution of the equation: log2x+log(x−5)=2

1. x= -4
2.x= 2
3.x= 10
4.x= 5

Answer 1

• 3.x= 10

Explanation:

• log 2x + log (x - 5) = 2
• log (2x(x - 5)) = 2
• 2x(x - 5) = 10²
• 2(x² - 5x) = 100
• x² - 5x - 50 = 0
• x² + 5x - 10x - 50 = 0
• x(x + 5) - 10(x + 5) = 0
• (x - 10)(x + 5) = 0
• x = 10
• x = -5, this root is discounted as log should be positive.

Correct choice is 3.