What does expand each logarithm mean?

Basic Log Rules & Expanding Log Expressions

Step-by-step explanation:

Expanding logarithms have rules that can be used to simplify (or, more correctly, to "condense") expressions, to "expand" expressions, or to solve for values.

In less formal terms, the log rules might be expressed as:

Multiplication inside the log can be turned into addition outside the log, and vice versa. Division inside the log can be turned into subtraction outside the log, and vice versa. An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.

Warning: Just as when you're dealing with exponents, the above rules work only if the bases are the same.