# What is meant by the "base" and "exponent" of a number and how do these relate to logarithms?

##### 1 Answer

**Exponentiation:**

Base Definition:

( for integer exponent values greater than or equal to zero )

example:

(#=243, if you're keeping track)

Note: based on this definition

Important Insight:

This insight is used to extend the definition of exponentiation to include negative and fractional exponents

Also

and

**Logarithms:**

Definition:

The value of

(Repeat that multiple times before going on. Come back to it as often as you need).

Example:

Common log identities:

Some special

- Sometimes you may see
#log (m)# written without a base specified; the convention in this case is that the base is#10# - Often you will see
#ln(m)# ; this is another form of the#log# function with a special base value,#e# ; that is

#ln(m) = log_e(m)#

where#e# is a special number (like#pi# ) approximately equal to#2.72# ;#e# has some special properties that make it useful in calculus.