9C - 9D Solving Exponential & Logarithmic Equations and Exponential Growth Content and lessons

Logarithm

A logarithm is the power to which a number (the base) must be raised to obtain another number.

Exponential Equation

An equation in which a variable appears in an exponent.

Changing Base Formula

A formula used to convert logarithms from one base to another: log_a(b) = log_c(b) / log_c(a).

Common Logarithm

A logarithm with base 10, often written simply as log.

Natural Logarithm

A logarithm with base e, denoted as ln.

Power Rule of Logarithms

The rule stating that log_b(a^c) = c * log_b(a).

Product Rule of Logarithms

The rule stating that log_b(m * n) = log_b(m) + log_b(n).

Quotient Rule of Logarithms

The rule stating that log_b(m / n) = log_b(m) - log_b(n).

Exponential Growth Equation

A formula to represent exponential growth: y = a * (1 + r)^t.

Exponential Decay Equation

A formula for exponential decay: y = a * (1 - r)^t.

Isolate the Variable

The process of manipulating an equation to solve for a specific variable.

Exponential Function

A function of the form f(x) = ab^x, where b is a positive real number.

Bacterial Growth

An example of exponential growth observed in populations of bacteria.

PH Calculation

An example of logarithmic application used in chemistry to calculate the acidity of solutions.

Richter Scale

A logarithmic scale used to measure the magnitude of earthquakes.

Scientific Calculator

A calculator that can perform functions involving logarithms and exponents.

Invalid Solution

A solution that, when tested, renders a negative argument in a logarithmic expression.