Combining or Condensing Logarithms
The reverse process of expanding logarithms is called combining or condensing logarithmic expressions into a single quantity. Other textbooks refer to this as simplifying logarithms. But, they all mean the same.
The idea is that you are given a bunch of log expressions as sums and/or differences, and your task is to put them back or compress into a “nice” one log expression.
I highly recommend that you review the rules of logarithms first before looking at the worked examples below because you’ll use them in reverse.
For instance, if you go from left to right of the equation then you must be expanding, while going from right to left then you must be condensing.
Rules of Logarithms
Study the description of each rule to get an intuitive understanding of it.
Descriptions of Logarithm Rules
Rule1: Product Rule
The logarithm of the product of numbers is the sum of logarithms of individual numbers.
Rule 2: Quotient Rule
The logarithm of the quotient of numbers is the difference of the logarithm of individual numbers.
Rule 3: Power Rule
The logarithm of an exponential number is the exponent times the logarithm of the base.
Rule 4: Zero Rule