For the following, assume that x, y, a, and b are all positive. Also assume that a ≠ 1, b ≠ 1.
1. loga x = N means that aN = x.
2. log x means log10 x. All loga rules apply for log. When a logarithm is written without a base it means common logarithm.
3. ln x means loge x, where e is about 2.718. All loga rules apply for ln. When a logarithm is written "ln" it means natural logarithm.
Note: ln x is sometimes written Ln x or LN x.
1. Inverse properties: loga ax = x and a(loga x) = x
2. Product: loga (xy) = loga x + loga y
4. Power: loga (xp) = p loga x
5. Change of base formula:
loga (x + y) ≠ loga x + loga y
loga (x – y) ≠ loga x – loga y