What is the value of $$x$$ in the equation $$3^3 = 3^{4x + 2}$$ ?

The value of $$x$$ is $$\frac{1}{4}$$ .

What is the first step in solving $$8 = 2^{5x + 7}$$ ?

The first step is to rewrite 8 as $$2^3$$ .

What is the principle of equating exponents in exponential equations?

If $$a^m = a^n$$ , then $$m = n$$ , provided that $$a$$ is not zero.

What is the relationship between exponential functions and their graphs?

Exponential functions have a characteristic curve that increases rapidly for positive exponents and approaches zero for negative exponents.

What is the importance of understanding bases in exponential equations?

Understanding bases is crucial because it allows you to manipulate and solve exponential equations effectively.

What is the general form of an exponential equation?

The general form of an exponential equation is $$a^x = b$$ , where $$a$$ and $$b$$ are constants.

How can you check your solution to an exponential equation?

You can check your solution by substituting it back into the original equation to see if both sides are equal.

What is the significance of the exponent in an exponential equation?

The exponent determines the rate of growth or decay in an exponential function.

Exponential Equations (no logs) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential equation?

Back

2.

FLASHCARD QUESTION

Front

How do you solve exponential equations?

Back

To solve exponential equations, you typically need to rewrite both sides of the equation with the same base, then set the exponents equal to each other.

3.

FLASHCARD QUESTION

Front

What is the base in an exponential expression?

Back

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