What is the property of logarithms that allows you to condense the expression $$\frac{1}{2}\text{log}_6a - \text{log}_6b + \text{log}_66$$ ?

The property states that $$\text{log}_b(m) - \text{log}_b(n) = \text{log}_b\frac{m}{n}$$ and $$k \text{log}_b(m) = \text{log}_b(m^k)$$ . Thus, the expression condenses to $$\text{log}_6\frac{6\text{sqrt}{a}}{b}$$ .

How do you expand the logarithm $$\text{log}_{}\frac{x^3}{y^4z}$$ using properties of logarithms?

Using the properties of logarithms, you can expand it as follows: $$\text{log}_{}(x^3) - \text{log}_{}(y^4) - \text{log}_{}(z) = 3\text{log}_{}(x) - 4\text{log}_{}(y) - \text{log}_{}(z)$$ .

What is the expanded form of $$\text{log}_6\frac{5x^3}{y}$$ ?

The expanded form is $$\text{log}_65 + 3\text{log}_6x - \text{log}_6y$$ .

How do you simplify the expression $$\frac{1}{2}\text{log}_964 + \text{log}_9x$$ ?

You can simplify it using the property of logarithms: $$\frac{1}{2}\text{log}_964 = \text{log}_9(8)$$ , so the expression simplifies to $$\text{log}_9(8x)$$ .

What is the expanded form of $$\text{log}_2igg(\frac{M^{1/3}N^4}{1}igg)$$ ?

The expanded form is $$\frac{1}{3}\text{log}_2M + 4\text{log}_2N$$ .

What is the power property of logarithms?

The power property states that $$\text{log}_b(m^k) = k \text{log}_b(m)$$ .

What is the change of base formula for logarithms?

The change of base formula states that $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any positive base $$k$$ .

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

The value of $$\text{log}_b(b) = 1$$ .

What is the value of $$\text{log}_b(1)$$ ?

The value of $$\text{log}_b(1) = 0$$ .

How do you express $$\text{log}_b(m^k)$$ in terms of $$\text{log}_b(m)$$ ?

You express it as $$k \text{log}_b(m)$$ .

What is the relationship between logarithms and exponents?

Logarithms are the inverse operations of exponentiation. If $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

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 $$\text{log}_b(a)$$ , $$b$$ is the base.

What does it mean to condense a logarithmic expression?

To condense a logarithmic expression means to combine multiple logarithmic terms into a single logarithm using the properties of logarithms.

(AA) Expanding & Condensing Self-Assessment Flashcards

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4.

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5.

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6.

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Define the product property of logarithms.

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7.

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Define the quotient property of logarithms.

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