8.4 – Properties of Logarithms

Properties of Logarithms There are four basic properties of logarithms that we will be working with. For every case, the base of the logarithm can not be equal to 1 and the values must all be positive (no negatives in logs)

Product Rule logbMN = LogbM + logbN Ex: logbxy = logbx + logby Ex: log6 = log 2 + log 3 Ex: log39b = log39 + log3b

Quotient Rule Ex:

Power Rule Ex:

Change of Base Rule

Let’s try some Working backwards now: write the following as a single logarithm.

Let’s try some Write the following as a single logarithm.

Let’s try something more complicated . . . Condense the logs log 5 + log x – log 3 + 4log 5

Let’s try something more complicated . . . Condense the logs log 5 + log x – log 3 + 4log 5

Let’s try something more complicated . . . Expand

Let’s try something more complicated . . . Expand