exponential equation
Definition
Noun: An equation in which the variable appears in an exponent. It is a mathematical statement that sets two expressions involving exponential functions equal to each other, where the unknown quantity is typically in the exponent's position.
Usage
An exponential equation is solved to find the value(s) of the variable that make the equation true. The solution often requires using logarithms or properties of exponents to isolate the variable.
Examples
- The equation is a simple exponential equation.
- Solving the exponential equation requires taking the natural logarithm of both sides.
- In the exponential equation , you can rewrite 25 as to find the solution.
Advanced Usage
- Compound Interest Formula: The formula for calculating investment growth is an example of an exponential equation when solving for the time or the rate .
- Radioactive Decay: The equation , used to model decay, becomes an exponential equation when solving for the decay constant or the time .
Variants and Related Words
- Exponential Function (n): A function of the form , where the independent variable is in the exponent. This is the type of function that appears in an exponential equation.
- Logarithmic Equation (n): An equation that involves logarithms of expressions containing the variable. These are often used to solve exponential equations.
Synonyms
- None that are direct, single-word synonyms. It is described as "an equation with the variable in the exponent."
Related Phrases
- Solve an exponential equation: The standard phrase for finding the solution.
- Exponential growth/decay equation: A specific type of exponential equation that models increasing or decreasing quantities at a rate proportional to their current value.
Related Idioms
- Not applicable for this technical mathematical term.
Noun
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an equation involving exponential functions of a variable
