# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 7

## Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 7

Published $1968$.

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## $7 \quad$ Exponential and Logarithmic Functions

### Laws of Exponents

$7.1$ Product of Powers
$7.2$ Quotient of Powers
$7.3$ Power of Power
$7.4$ Zeroth Power of Real Number equals One
$7.5$ Exponent Combination Laws/Negative Power
$7.6$ Power of Product
$7.7$ Definition:Root (Analysis)
$7.8$ Definition:Power (Algebra)/Rational Number
$7.9$ Root of Quotient equals Quotient of Roots

### Logarithms and Antilogarithms

Definition:General Logarithm/Positive Real
Definition:Logarithm/Base

### Laws of Logarithms

$7.10$ Sum of Logarithms/General Logarithm
$7.11$ Difference of Logarithms
$7.12$ Logarithm of Power/General Logarithm

### Natural Logarithms and Antilogarithms

Definition:General Logarithm/Common
Definition:Natural Logarithm/Positive Real/Definition 2

### Change of Base of Logarithms

$7.13$ Change of Base of Logarithm
$7.14$ Change of Base of Logarithm/Base 10 to Base e/Form 1
$7.15$ Change of Base of Logarithm/Base e to Base 10/Form 1

### Relationship between Exponential and Trigonometric Functions

$7.16$ Euler's Formula/Real Domain
$7.16$ Euler's Formula/Real Domain/Corollary
$7.17$ Sine Exponential Formulation/Real Domain
$7.18$ Cosine Exponential Formulation/Real Domain
$7.19$ Tangent Exponential Formulation/Formulation 2
$7.19$ Tangent Exponential Formulation/Formulation 3
$7.20$ Cotangent Exponential Formulation
$7.21$ Secant Exponential Formulation
$7.22$ Cosecant Exponential Formulation

### Periodicity of Exponential Functions

$7.23$ Periodicity of Complex Exponential Function

### Polar Form of Complex Numbers expressed as an Exponential

$7.24$ Definition:Complex Number/Polar Form/Exponential Form

### Operations with Complex Numbers in Polar Form

$7.25$ Product of Complex Numbers in Exponential Form
$7.26$ Division of Complex Numbers in Exponential Form
$7.27$ De Moivre's Formula/Exponential Form
$7.28$ Roots of Complex Number/Exponential Form

### Logarithm of a Complex Number

$7.29$ Definition:Natural Logarithm/Complex/Definition 1

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