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

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

Published $\text {1968}$.

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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
$7.7$ Root (Analysis)
$7.8$ Rational Power
$7.9$ Root of Quotient equals Quotient of Roots

### Logarithms and Antilogarithms

Real General Logarithm
Base of Logarithm

### 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

Common Logarithm
Real Natural Logarithm

### Change of Base of Logarithms

$7.13$ Change of Base of Logarithm
$7.14$ Change of Base of Logarithm: Base $10$ to Base $e$
$7.15$ Change of Base of Logarithm: Base $e$ to Base $10$

### 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

$7.24$ Exponential Form of Complex Number

### 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

$7.29$ Complex Natural Logarithm

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