Three properties do all the work: multiply becomes add, divide becomes subtract, exponent becomes a multiplier. They are not arbitrary — each one is just what happens to a stack of factors. See why first, then watch one worked step at a time.
Look inside the log first
The three properties
Every one of these needs b > 0, b ≠ 1, M > 0, N > 0. And there is no rule for a sum inside a log: log(3 + 5) = log 8 ≈ 0.9031, but log 3 + log 5 ≈ 1.1761. Different numbers. Leave sums alone.
The three propertieschoose a direction to begin
Worked steps
Check it with numbers — drag and watch every line stay equal