To expand logarithms, write them as a sum or difference of logarithms where the power rule is applied if necessary. Often, using the rules in the order quotient rule, product rule, and then power rule will be helpful. To simplify logarithms, write them as a single logarithm.
Natural logarithms can be indicated either as: Ln(x) or loge(x). Changing the base of the log changes the result by a multiplicative constant. To convert from Log10 to natural logs, you multiply by 2.303. Analogously, to convert in the other direction, you divide by 2.303.
The common logarithm has base 10, and is represented on the calculator as log(x). The natural logarithm has base e, a famous irrational number, and is represented on the calculator by ln(x). The natural and common logarithm can be found throughout Algebra and Calculus.