Grouping of more than two numbers to perform basic aritmetic operations of addition/multiplication does not affect the final result.
The distributive property defines that the product of a single term and a sum or difference of two or more terms inside the bracket is same as multiplying each addend by the single term and then adding or subtracting the products.
The log of a product is equal to the sum of the log of the first base and the log of the second base:
The log of a quotient is equal to the difference of the logs of the numerator and denominator:
The log of a power is equal to the power times the log of the base:
The log of a new base is the log of the new base divided by the log of the old base in the new base: