## 10.1 Outline

- Exponential equation
- definition
- evaluate exponentials

- Definition of logarithm
- notation, logarithm, and argument
- common logarithm
- natural logarithm

- Evaluating logarithms
- evaluate
- using calculators
- change of base
- exact solution

- Exponential equations
- three types
- base 10
- base
*e* - base
*b*

2. micometer

- three types

## 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 log_{10}*x
*

**natural logarithm**is base

*e*; ln

*x*means log

_{e }xIn order to change from one base to another, use log* _{a}x* = log

*log*

_{b}x/

_{b}a.**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