Two Common Bases for Logarithms
Because we use a base 10 number system, we often wonder, “How can I write x as a power of 10?” In other words, we want to compute 
. Since this computation occurs frequently, we abbreviate by “log x.”
The base e occurs frequently in formulas describing growth and decay. We often wish to know the rate of growth, which is an exponent on e. (See the tutorial Real-World Applications of Exponential Functions for more details.) Thus 
is another common computation. This logarithm is often called the natural logarithm; we may write “ln x” to mean “” (the notation ln comes from the French, “logarithm naturale”).
CAUTION: Because natural logarithms occur so frequently, some calculators, computer algebra systems, and textbooks use “log x” or “Log x” to indicate the natural logarithm “ln x.” Be sure to perform a test calculation like “log e =” to verify the syntax used by your technology.
Most calculator and computer algebra systems do not compute logarithms in bases other than e and 10. To find these values, we will employ the Change of Base Formula.
