Expand $$\text{log}(xy^2)$$ using logarithmic properties.

$$\text{log}(xy^2) = \text{log}(x) + 2\text{log}(y)$$ .

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

$$\text{log}igg(\frac{x}{y}igg) = \text{log}(x) - \text{log}(y)$$ .

Expand $$\text{log}(4x)$$ using logarithmic properties.

$$\text{log}(4x) = \text{log}(4) + \text{log}(x)$$ .

Expand $$\text{log}(3x)^2$$ using logarithmic properties.

$$\text{log}(3x)^2 = 2(\text{log}(3) + \text{log}(x))$$ .

Expand $$\text{log}igg(\frac{m^3}{n}igg)$$ using logarithmic properties.

$$\text{log}igg(\frac{m^3}{n}igg) = 3\text{log}(m) - \text{log}(n)$$ .

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. For example, in $$\text{log}_b(a) = c$$ , b is the base.

Define a common logarithm.

A common logarithm is a logarithm with base 10, denoted as $$\text{log}(x)$$ .

Define a natural logarithm.

A natural logarithm is a logarithm with base e (approximately 2.718), denoted as $$\text{ln}(x)$$ .

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

How do you convert from exponential form to logarithmic form?

To convert from exponential form $$b^x = y$$ to logarithmic form, write $$x = \text{log}_b(y)$$ .

How do you convert from logarithmic form to exponential form?

To convert from logarithmic form $$x = \text{log}_b(y)$$ to exponential form, write $$b^x = y$$ .

What is the significance of logarithms in solving exponential equations?

Logarithms are used to solve exponential equations by allowing us to bring the exponent down, making it easier to isolate the variable.

Condensing and Expanding Logs Flashcards

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1.

FLASHCARD QUESTION

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Define the product property of logarithms.

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2.

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What is the quotient property of logarithms?

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3.

FLASHCARD QUESTION

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State the power property of logarithms.

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4.

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5.

FLASHCARD QUESTION

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6.

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