How do you solve an exponential equation of the form $$a^x = b$$ ?

Take the logarithm of both sides: $$x = \frac{\text{ln}(b)}{\text{ln}(a)}$$ .

How do you express $$4^{2x} = 19$$ in logarithmic form?

You can express it as $$x = \frac{\text{log}_4(19)}{2}$$ .

What is the logarithmic identity for $$\text{ln}(a^b)$$ ?

The identity states that $$\text{ln}(a^b) = b \times \text{ln}(a)$$ .

What is the result of $$\text{ln}(1)$$ ?

The result is 0, since e^0 = 1.

What is the relationship between exponential and logarithmic functions?

Exponential functions are the inverse of logarithmic functions. If $$y = a^x$$ , then $$x = \text{log}_a(y)$$ .

What is the property of logarithms that allows you to combine the logarithm of a product?

The property states that $$\text{ln}(a \times b) = \text{ln}(a) + \text{ln}(b)$$ .

How do you solve $$e^x = 9$$ for x?

Take the natural logarithm of both sides: $$x = \text{ln}(9)$$ .

What is the solution to the equation $$4^{2x} = 19$$ ?

The solution is $$x = \frac{\text{log}_4(19)}{2}$$ .

What is the result of $$\text{ln}(e)$$ ?

The result is 1, since e^1 = e.

What is the property of exponents that states $$a^{m-n} = \frac{a^m}{a^n}$$ ?

This property allows you to subtract exponents when dividing exponential expressions with the same base.

LT 3c Solving Exponential Equations Flashcards

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1.

FLASHCARD QUESTION

Front

What is the natural logarithm of a number?

Back

The natural logarithm, denoted as ln, is the logarithm to the base e, where e is approximately equal to 2.71828. It is used to solve equations involving exponential growth.

2.

FLASHCARD QUESTION

Front

What property of logarithms allows you to expand the logarithm of a quotient?

Back

3.

FLASHCARD QUESTION

Front

What happens to exponents when two exponential expressions with the same base are multiplied?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.71828.

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