An exponential equation is an equation in which the variable appears in the exponent. It has the general form $a^x = b$ where $a$ and $b$ are constants.
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To solve exponential equations, you often use logarithms to isolate the variable.
If the bases of an exponential equation are the same, you can set the exponents equal to each other.
The natural logarithm (ln) is frequently used when solving exponential equations with base $e$.
Exponential growth and decay can be modeled using exponential equations.
Graphing exponential functions can help visualize solutions to exponential equations.
Review Questions
How do you solve an exponential equation if the bases are not the same?
What role do logarithms play in solving exponential equations?
Explain how you would graphically determine the solution to an exponential equation.
Related terms
Logarithmic Equation: An equation that involves a logarithm with a variable inside its argument, often solved by exponentiating both sides.
Natural Logarithm: $\text{ln}(x)$ is the logarithm to the base $e$, where $e \approx 2.718$. Commonly used in solving exponential equations with base $e$.
$e$ (Euler's Number): $e$ is an irrational constant approximately equal to 2.71828, and it serves as the base for natural logarithms.