Answer: x = {-4, 5}
Step-by-step explanation:
log (10x + 200) = log (x²) + log (10)
log (10x + 200) = log (10x²)
10x + 200 = 10x²
0 = 10x² - 10x - 200
0 = x² - x - 20
0 = (x - 5)(x + 4)
0 = x - 5 0 = x + 4
x = 5 x = -4
Check for extraneous solutions:
10x + 200 > 0 x² > 0
x = 5 10(5) + 200 > 0 (5)² > 0 both are satisfied
x = -4 10(-4) + 200 > 0 (-4)² > 0 both are satisfied
Both solutions are valid!
