log equation :)

Question

log₄(x²+3x)-log₄(x+5)=1

Answer 1

log₄ (x² + 3x) - log₄ (x+5) = 1

 

log₄ [(x² + 3x)/(x + 5)] = log₄ 4

 

(x² + 3x)/(x + 5) = 4

 

x² + 3x = 4x + 20

 

x² - x - 20 = 0

 

(x + 4)(x - 5) = 0

 

x = -4 or x = 5.

 

Plugging these into the original equation shows that they both work.