Question

Express as a single log:
1/2log5 x+2log5(x+2)-[log5(1+x)+log5(1-x)]

Answer 1

When you say log5 do you mean that 5 is the base of the log?

Answer 2

Here are the four essential log identities:
\[\log a + \log b = \log (ab)\]
\[\log a - \log b = \log (a/b)\]
\[a \log b = \log b ^{a}\]
\[\log _{a}b = (\log b) / (\log a)\]
The second two follow from the first one. All log problems are just applying one of these rules at the right time.