Section 10.1: Exponential Equations

10.1 Outline

1. Exponential equation
   1. definition
   2. evaluate exponentials
2. Definition of logarithm
   1. notation, logarithm, and argument
   2. common logarithm
   3. natural logarithm
3. Evaluating logarithms
   1. evaluate
   2. using calculators
   3. change of base
   4. exact solution
4. Exponential equations
   1. three types
      1. base 10
      2. base e
      3. base b

      2. micometer

10.1 Essential Ideas

An equation of the form b^x = N in which an unknown value is included as part of the exponent is called an exponential equation.  For positive b and A, b not equal to 1, x = log_b A; x is called the logarithm and A is called the argument.

common logarithm is base 10; log x means log₁₀x
natural logarithm is base e; ln x means log_e x

In order to change from one base to another, use log_ax = log_bx/log_ba.

Exponential equations fall into one of three types:

base 10; 10^x = 5
base e; e^–0.06x = 3.456
base b (arbitrary base); 8^x = 156.8