Chapter 18: Exponential and
Logarithmic Functions
Exponential and logarithmic functions play a significant role in
algebra, modeling a wide range of phenomena in science,
finance, and beyond. This chapter explores the basics of these
functions, their properties, and how to solve related equations.
Introduction to Exponents and Logarithms
Exponential functions have the form \( f(x) = a \cdot b^x \),
where \( a \) is the initial value, \( b \) is the base of the
exponential, and \( x \) is the exponent. They are characterized
by rapid growth or decay, depending on the base.
Logarithmic functions, the inverse of exponential functions,
have the form \( g(x) = \log_b(x) \), where \( b \) is the base of
the logarithm, and \( x \) is the value. These functions grow
more slowly and are used to solve for the exponent in
exponential equations.
Rules of Exponents and Logarithms
Both exponential and logarithmic functions follow specific rules
that facilitate their manipulation and solution: -
- Exponent Rules: These include the power rule (\( a^{m
\cdot n} = a^m \times a^n \)), the product rule (\( a^m
\times a^n = a^{m + n} \)), and the quotient rule (\( a^m /
a^n = a^{m - n} \)).
Logarithmic Functions
Exponential and logarithmic functions play a significant role in
algebra, modeling a wide range of phenomena in science,
finance, and beyond. This chapter explores the basics of these
functions, their properties, and how to solve related equations.
Introduction to Exponents and Logarithms
Exponential functions have the form \( f(x) = a \cdot b^x \),
where \( a \) is the initial value, \( b \) is the base of the
exponential, and \( x \) is the exponent. They are characterized
by rapid growth or decay, depending on the base.
Logarithmic functions, the inverse of exponential functions,
have the form \( g(x) = \log_b(x) \), where \( b \) is the base of
the logarithm, and \( x \) is the value. These functions grow
more slowly and are used to solve for the exponent in
exponential equations.
Rules of Exponents and Logarithms
Both exponential and logarithmic functions follow specific rules
that facilitate their manipulation and solution: -
- Exponent Rules: These include the power rule (\( a^{m
\cdot n} = a^m \times a^n \)), the product rule (\( a^m
\times a^n = a^{m + n} \)), and the quotient rule (\( a^m /
a^n = a^{m - n} \)).
