Найдите корень уравнения log₈(x+4)=log₈(5x-16)

Question

Найдите корень уравнения log₈(x+4)=log₈(5x-16)

Answer 1

Так как основания одинаковы, то получим:

x+4=5x-16

4x=20

x=5

Answer 2

(log(x+4))/(log(8)) = (log(5 x-16))/(log(8))

 (log(x+4))/(log(8))-(log(5 x-16))/(log(8)) = 0

 (log(x+4)-log(5 x-16))/(log(8)) = 0

log(x+4)-log(5 x-16) = 0

log(x+4)-log(5 x-16) = log(1/(5 x-16))+log(x+4) = log((x+4)/(5 x-16)):

log((x+4)/(5 x-16)) = 0

 (x+4)/(5 x-16) = 1

x+4 = 5 x-16

-4 x = -20

| x = 5