Uploaded April 2026 | Updated September 2026, 2 weeks ago
Although the base of a logarithmic function can be any positive real number other than "one", the base values most commonly used for logarithms are base ten - otherwise known as the “common logarithm” and “base e” - the “natural logarithm”. Scientific calculators can typically calculate logarithms with a base of ten or e. However, we may want to find the log of that same number with a base other than ten or e. In that case, we can use what is called the "change of base" formula which can calculate the log of a number for any arbitrary base. In this lecture, we will see how to use this formula, to convert the base of any logarithm to any other base.
Although the base of a logarithmic function can be any positive real number other than "one", the base values most commonly used for logarithms are base ten - otherwise known as the “common logarithm” and “base e” - the “natural logarithm”. Scientific calculators can typically calculate logarithms with a base of ten or e. However, we may want to find the log of that same number with a base other than ten or e. In that case, we can use what is called the "change of base" formula which can calculate the log of a number for any arbitrary base. In this lecture, we will see how to use this formula, to convert the base of any logarithm to any other base.
