What are logarithms and how do you manipulate them?

A logarithms are the 3rd way of representing the interactions between bases and powers.To start we will cover basic algebra about powers or exponents. base^exponent = answer , 3² = 9This is the same as writing:^exponent√ answer = base, ²√ 9 = 3But what happens if we only have a base and an answer? We find the exponent using an logarithm:log _base(answer) = exponent , log₃(9) = 2
There is several rules that logarithms have, these are called the Log Laws.1.BasicsThe easiest logs to solve are ones where the answer is 1.e.g. log _x ( 1 ) = 0 , x can be any number except zeroBecause : x ⁰ = 1 The second easiest 2. Adding and subtractingIn order to add two logs together their bases must be the same. Adding to logs together looks like this: log₂(3) + log₂(5) = log₂ ( 3 * 5) , notice the answers for the first to logs are multiplied together.