The following examples need to be solved using the Laws of Logarithms and change of base. So please remember the laws of logarithms and the change of the base of logarithms.

These laws together with the definition of a logarithm can be used to simplify and evaluate logarithmic expressions and to solve equations involving logarithms.

In solving problems of the second type earlier, in most of the cases, we take recourse to the basic defini-tion of logarithms (which is very important and should be memorized).

In general, expressions of the form am are called indices, where a is called the base and m is called the index or exponent or power and it is read as “a exponent m” or “a to the power of m”.

Oct 14, 2025 · Index (plural: indices) is a numerical exponent in mathematics that shows how many times a base number is multiplied by itself. Logarithm (or log) is a mathematical …

Reading logarithms from the tables is the same as reading squares square roots and reciprocals. We can read logarithms of numbers between 1 and 10 directly from the table.

Logarithms can be used to solve equations such as 2 x = 3, for x. In senior mathematics, competency in manipulating indices is essential, since they are used extensively in both …