Define the property of logarithms that allows the simplification of $$\frac{1}{2}\text{log}_9 64 + \text{log}_9 x$$ .

The property states that $$a \text{log}_b c = \text{log}_b(c^a)$$ , allowing us to rewrite $$\frac{1}{2}\text{log}_9 64$$ as $$\text{log}_9(64^{1/2}) = \text{log}_9(8)$$ .

What is the condensed form of $$\frac{1}{2}\text{log}_6 a - \text{log}_6 b + \text{log}_6 6$$ ?

The condensed form is $$\text{log}_6igg(\frac{6\text{sqrt}{a}}{b}igg)$$ , using the properties of logarithms.

Expand $$\text{log}_6igg(\frac{5x^3}{y}igg)$$ using logarithmic properties.

The expansion is $$\text{log}_6 5 + 3\text{log}_6 x - \text{log}_6 y$$ .

What is the expansion of $$\text{log}_2igg(\frac{x^3}{y^4 z}igg)$$ ?

The expansion is $$3\text{log}_2 x - 4\text{log}_2 y - \text{log}_2 z$$ .

What is the result of $$\text{log}_b (x^n)$$ ?

The result is $$n \text{log}_b x$$ , showing that the logarithm of a power is the exponent times the logarithm.

How do you simplify $$\text{log}_9 64 + \text{log}_9 x$$ ?

You can simplify it to $$\text{log}_9(64x)$$ using the product property of logarithms.

What is the value of $$\text{log}_b b$$ ?

The value is 1, since any number raised to the power of 1 equals itself.

Define the term 'base' in logarithms.

The base is the number that is raised to a power to obtain a given number, denoted as $$b$$ in $$\text{log}_b a$$ .

What is the relationship between logarithms and exponents?

Logarithms are the inverse operations of exponentiation, meaning $$\text{log}_b a = c$$ is equivalent to $$b^c = a$$ .

What does $$\text{log}_b 1$$ equal?

It equals 0, since any number raised to the power of 0 equals 1.

How do you express $$\text{log}_b (x^m y^n)$$ in expanded form?

It can be expressed as $$m \text{log}_b x + n \text{log}_b y$$ .

What is the significance of the logarithm of a number less than 1?

The logarithm of a number less than 1 is negative, indicating that the exponent needed to reach that number is negative.

(AA) Expanding & Condensing Self-Assessment Flashcards

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3.

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4.

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5.

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State the change of base formula for logarithms.

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6.

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This property states that the logarithm of a product is the sum of the logarithms.

7.

FLASHCARD QUESTION

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This property indicates that the logarithm of a quotient is the difference of the logarithms.

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