2log5 x+log5 100−2=0

Question

2log5 x+log5 100−2=0

Answer 1

2log5 (x) + log5 (100) - 2 = 0
log5 (x^2) + log5 (100) = 2
log5 (x^2*100) = 2
x^2*100 = 25
x^2 = 0,25
x = ±0,5
ОДЗ х>0, поэтому х = 0,5

Answer 2

2 log(5)x+log(5)100-2=0 ;x>0
2log(5)x+2 log(5)10-2=0

log(5)х+log(5)10-1=0
log(5)x+log(5)2+log(5)5-1=0
log(5)x+log(5)2=0
log(5)x=-log(5)2
ĺog(5)x=log(5)2^(-1)
x=1/2