Log5(x+3)+log x+3 5=2

Question

Log5(x+3)+log x+3 5=2

Answer 1

Log5(x+3)+logx+3(5)=2       ОДЗ x+3>0 x>-3  и x+3≠1  x≠-2
свойство логарифма loga(b)=1/logb(a)
log5(x+3)+1/log5(x+3)=2
log5(x+3)=a 
a+1/a=2
a^2+1=2a
a^2-2a+1=0
(a-1)^2=0
a=1
log5(x+3)=1
log5(x+3)=log5(5)
x+3=5
x=2