What is the base of an exponential function?

The base of an exponential function is the constant value raised to a variable exponent, typically denoted as $$a^x$$ , where $$a$$ is the base.

What is the inverse operation of an exponential function?

The inverse operation of an exponential function is the logarithm, which allows you to solve for the exponent in equations of the form $$a^x = b$$ .

Define the logarithmic form of an exponential equation.

The logarithmic form of an exponential equation $$a^x = b$$ is written as $$\text{log}_a(b) = x$$ , meaning the exponent x is the power to which the base a must be raised to produce b.

What is the change of base formula for logarithms?

The change of base formula states that $$\text{log}_a(b) = \frac{\text{log}_c(b)}{\text{log}_c(a)}$$ for any positive base c.

What is the significance of the number e in exponential equations?

The number e (approximately 2.718) is the base of natural logarithms and is significant in continuous growth or decay processes, often used in calculus and complex exponential equations.

What is the relationship between exponential growth and decay?

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

Solving Exponential Equations Flashcards

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1.

FLASHCARD QUESTION

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Define an exponential equation.

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2.

FLASHCARD QUESTION

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This property is known as the Product of Powers Property, which states that when multiplying two exponential expressions with the same base, you can add the exponents.

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