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 of Number

$7.8$ 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)

$7.17$ Euler's Sine Identity: Real Domain

$7.18$ Euler's Cosine Identity: Real Domain

$7.19$ Euler's Tangent Identity:Formulation 2

$7.19$ Euler's Tangent Identity: Formulation 3

$7.20$ Euler's Cotangent Identity

$7.21$ Euler's Secant Identity

$7.22$ Euler's Cosecant Identity

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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