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Solve. Round solution to the fourth decimal place

log5(7x)+log5(x)=3

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2 Answers

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
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!!!!!!!!!!!!!!!!!!!!!!!!!