Log5 (4-x)+log5 ( x+3)=log5 10

Question

Log5 (4-x)+log5 ( x+3)=log5 10

Answer 1

Log5 (4-x) + log5 (x+3) = log5 10 , x∈(-3,4)
log5 (4-x)(x+3)= log5 10
(4-x)(x+3)=10
4x+12-x²-3x=10
-x²+x+12-10=0
-x²+x+2=0
x²-x-2=0
(x-2)(x+1)=0

(a.b=0⇔a=0 ∨ b=0)

a)x-2=0, x=2 , 2∈(-3,4)
b)x+1=0,x=-1, -1∈(-3,4)

Otvet: x=2, x=-1