College Algebra & Trigonometry, 2018a

3.2. LOGARITHMIC NOTATION 161
3.2 Logarithmic Notation
A Logarithm is an exponent. In the early 1600’s, the Scottish mathematician John
Napier devised a method of expressing numbers in terms of their powers of ten
in order simplify calculation. Since the advent of digital calculators, the methods
of calculation using logarithms have become obsolete, however the concept of
logarithms continues to be used in many area of mathematics.
The fundamental idea of logarithmic notation is that it is simply a restatement of
an exponential relationship. The definition of a logarithm says:
log b N = x → b x = N
The notation above would be read as ”log to the base b of N equals x means that
b to the x power equals N.” In this section we will focus mainly on becoming
familiar with this notation. In later sections, we will learn to use this process to
solve equations.
Example
Express the given statement using exponential notation:
log 2 32=5
If log 2 32 = 5, then 2 5 =32.
Example
Express the given statement using exponential notation:
log 7 4 ≈ 0.7124
If log 7 4 ≈ 0.7124, then 7 0.7124 ≈ 4
If the logarithm notation appears without a base, it is usually assumed that the
base should be 10.