How do you simplify $$3^4 \times 3^8$$ ?

Use the property of exponents: $$a^m \times a^n = a^{m+n}$$ . Therefore, $$3^4 \times 3^8 = 3^{4+8} = 3^{12}$$ .

What is the formula for expanding a logarithm of a fraction, such as $$\log_2 \frac{x^2y}{z}$$ ?

Use the property: $$\log_b \frac{m}{n} = \log_b m - \log_b n$$ . Thus, $$\log_2 \frac{x^2y}{z} = \log_2(x^2y) - \log_2(z) = 2\log_2x + \log_2y - \log_2z$$ .

What is the power rule for logarithms?

The power rule states that $$\log_b(m^n) = n \cdot \log_b(m)$$ .

How do you solve for x in $$\log_3 27 = x$$ ?

Convert to exponential form: $$3^x = 27$$ . Since $$27 = 3^3$$ , we have $$x = 3$$ .

What is the product rule for logarithms?

The product rule states that $$\log_b(m \cdot n) = \log_b(m) + \log_b(n)$$ .

What is the definition of an exponential function?

An exponential function is a mathematical function of the form $$f(x) = a \cdot b^x$$ , where $$a$$ is a constant, $$b$$ is the base, and $$x$$ is the exponent.

What does it mean for a function to shift horizontally?

A horizontal shift involves moving the graph of the function left or right, which can be represented by changing the input variable.

What is the zero exponent rule?

The zero exponent rule states that any non-zero number raised to the power of zero equals one: $$a^0 = 1$$ .

How do you express $$3^4 \times 3^8$$ in terms of a single exponent?

Combine the exponents: $$3^4 \times 3^8 = 3^{4+8} = 3^{12}$$ .

What is the significance of the vertical shift in the function $$f(x) = 2^x + 3$$ ?

The vertical shift indicates that the entire graph of the function is moved up by 3 units, affecting the function's range.

Flashcard 5 & 6 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the relationship between exponents and logarithms?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

Adding a constant shifts the graph vertically. In this case, the function shifts up by 3 units.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the base of a logarithm?

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a function to be transformed vertically?

Back

A vertical transformation involves shifting the graph of the function up or down without changing its shape.

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