How do you expand $$\text{log}_2igg(\frac{x^2}{4}igg)$$ ?

Using the properties of logarithms, $$\text{log}_2igg(\frac{x^2}{4}igg) = \text{log}_2(x^2) - \text{log}_2(4) = 2\text{log}_2(x) - 2$$ .

What is the expanded form of $$\text{log}_8(x^6y^3)$$ ?

Using the properties of logarithms, $$\text{log}_8(x^6y^3) = 6\text{log}_8(x) + 3\text{log}_8(y)$$ .

How do you condense $$\text{log}4 + 3\text{log}(x) + \text{log}(y)$$ into a single logarithm?

Using the properties of logarithms, $$\text{log}4 + 3\text{log}(x) + \text{log}(y) = \text{log}(4x^3y)$$ .

What is the value of $$\text{log}_3(20)$$ using the change of base formula?

Using the change of base formula, $$\text{log}_3(20) = \frac{\text{log}(20)}{\text{log}(3)}$$ , which evaluates to approximately 2.727.

What does $$\text{log}_a(a)$$ equal?

$$\text{log}_a(a) = 1$$ , because a raised to the power of 1 equals a.

What does $$\text{log}_a(1)$$ equal?

$$\text{log}_a(1) = 0$$ , because a raised to the power of 0 equals 1.

How do you express $$\text{log}_b(m^n)$$ ?

Using the power rule, $$\text{log}_b(m^n) = n\text{log}_b(m)$$ .

What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a given number. In $$\text{log}_a(b)$$ , 'a' is the base.

What is the relationship between exponential and logarithmic functions?

Exponential functions can be expressed as logarithmic functions. For example, if $$y = a^x$$ , then $$x = \text{log}_a(y)$$ .

What is the domain of a logarithmic function?

The domain of a logarithmic function $$\text{log}_a(x)$$ is all positive real numbers, i.e., $$x > 0$$ .

What is the range of a logarithmic function?

The range of a logarithmic function $$\text{log}_a(x)$$ is all real numbers, i.e., $$(-\text{∞}, \text{∞})$$ .

What is the significance of the logarithm base being greater than 1?

If the base of a logarithm is greater than 1, the function is increasing; if the base is between 0 and 1, the function is decreasing.

Expand and Condense Logs Flashcard 7-6(Honors) Flashcards

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1.

FLASHCARD QUESTION

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What is the change of base formula for logarithms?

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6.

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What is the property of logarithms that allows you to combine logs with addition?

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7.

FLASHCARD QUESTION

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What is the property of logarithms that allows you to combine logs with subtraction?

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