Solve the following logarithm equation. Please show all of your work.

Question

log (5 + x) – log(x – 2) = log 2

Answer 1

log (5 + x) – log(x – 2) = log 2
log [(5+x)/(x-2)] = log 2

(5+x)/(x-2) = 2
2x - 4 = 5+x
x = 9

Answer 2

Use law of logarithms,
log(a)-log(b)=log(a/b)

So
log (5 + x) – log(x – 2) = log 2
=log((5+x)/(x-2))=log2
Take anti-log on both sides
(5-x)/(x-2)=2
(5-x)=2(x-2)
Solve for x.

Answer 3

(5+x)/(x-2)=2

5+x=2*(x-2)

5+x=2x-4

5+4=2x-x

9=x

x=9

Answer 4

−6ln(x) − 8ln(y) +
1
8
ln(z)