Solve. Round solution to the fourth decimal place

Question

log₅(7x)+log₅(x)=3

Answer 1

log₅(7x)+log₅(x)=3

log₅(7x*x)=3

log₅(7x²)=3

5³=7x²

125=7x²

125/7=x²

17.85714=x²

√17.85714=x

4.2258=x

Answer 2

log5(7x)+log5(x)=3 is the equation, this may be transformed to log5 (7) + log5 (x) +log5 (x) =3 =>

2 log5 (x) = 3 - log5 (7) = 3-(log10(7)/log10(5)) = 3-1.2091= 1.7909=2log5 (x) =>

log5(x) = 1.7909/2= 0.8955

log (x)/log 5 = 0.8955

log (x) = 0.8955*0.6989 = 0.6258

x = log‾¹ 0.6258 = 4.2247

CHECK!!!!!!!!!!!!!!!!!!!!!!!!!