Question

Use the product rule for logarithms to find all x values such that log 5 ( 2 x + 1 ) + log 5 ( x + 3 ) = 2

Answer 1

x = -5.5, 2

Explanation:

log₅ (2x + 1) + log₅ (x+3) = 2

log₅ ((2x + 1)(x+3)) = 2

log₅ (2x² + 7x + 3) = 2

2x² + 7x + 3 = 25

2x² + 7x - 22 = 0

x² + 3.5x - 11 = 0

(x + 11/2) (x - 2) = 0

x = -5.5, 2