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

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