Math  Logarithm
posted by Armando .
Solve the following logarithm equation. Please show all of your work.
log (5 + x) – log(x – 2) = log 2

log (5 + x) – log(x – 2) = log 2
log [(5+x)/(x2)] = log 2
(5+x)/(x2) = 2
2x  4 = 5+x
x = 9 
Use law of logarithms,
log(a)log(b)=log(a/b)
So
log (5 + x) – log(x – 2) = log 2
=log((5+x)/(x2))=log2
Take antilog on both sides
(5x)/(x2)=2
(5x)=2(x2)
Solve for x. 
(5+x)/(x2)=2
5+x=2*(x2)
5+x=2x4
5+4=2xx
9=x
x=9 
−6ln(x) − 8ln(y) +
1
8
ln(z)