Question

log (5+x)-log (x-3)=log 3

Answer 1

loga-logb =log(a/b)
next step cancel logs and slove for x

Answer 2

Do not EVER "cancel logs". That doesn't mean anything.

After using the logarithm property, \(\log(5+x) - \log(x-3) = \log\left(\dfrac{5+x}{x-3}\right)\)...

Note that if \(\log(a) = \log(b)\;then\;a = b\), since the logarithm is monotonic increasing. This leads to...

\(\dfrac{5+x}{x-3} = 3\)

Thinking about Domain issues. In the original problem statement, we have...

\(5+x > 0 \longrightarrow x > -5\)
\(x-3 > 0 \longrightarrow x > 3\)

Remembering that, whatever else happens, do NOT accept a result of 3 or less. It is wrong.