Rewrite $$\log_5(55)$$ as the sum of two logarithms.

$$\log_5(55) = \log_5(11) + \log_5(5)$$ .

Rewrite $$\log_b(xy)$$ as two logs.

$$\log_b(xy) = \log_b(x) + \log_b(y)$$ .

Condense the logarithm expression: $$2\log_8(a) - (\log_8(c) + 3\log_8(b))$$ .

$$\log_8\left(\frac{a^2}{b^3c}\right)$$ .

Rewrite $$\log_b(x/y)$$ as two logs.

$$\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$$ .

What is the change of base formula for logarithms?

The change of base formula states that $$\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$$ for any base k.

What is the definition of a logarithm?

A logarithm is the exponent to which a base must be raised to produce a given number, expressed as $$\log_b(a) = c$$ if $$b^c = a$$ .

If $$\log_b(a) = c$$ , what is the equivalent exponential form?

The equivalent exponential form is $$b^c = a$$ .

What is the value of $$\log_2(8)$$ ?

$$\log_2(8) = 3$$ because $$2^3 = 8$$ .

What is the value of $$\log_5(25)$$ ?

$$\log_5(25) = 2$$ because $$5^2 = 25$$ .

If $$\log_b(x) = 0$$ , what can we conclude about x?

If $$\log_b(x) = 0$$ , then $$x = 1$$ because $$b^0 = 1$$ .

What is the value of $$\log_7(49)$$ ?

$$\log_7(49) = 2$$ because $$7^2 = 49$$ .

Properties of Logarithms Practice Flashcards

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1.

FLASHCARD QUESTION

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What is the product property of logarithms?

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2.

FLASHCARD QUESTION

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What is the quotient property of logarithms?

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3.

FLASHCARD QUESTION

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What is the power property of logarithms?

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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6.

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7.

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