What is the property of logarithms used to condense $$2\log_6(a) + \log_6(b) - 3\log(c)$$ ?

Use the properties: $$n\log_b(a) = \log_b(a^n)$$ and $$\log_b(a) + \log_b(c) = \log_b(ac)$$ to condense to $$\log_6\left(\frac{a^2b}{c^3}\right)$$ .

Evaluate $$\log_2(32)$$ .

The value is 5, since $$2^5 = 32$$ .

What is the product property of logarithms?

The product property states that $$\log_b(mn) = \log_b(m) + \log_b(n)$$ .

What is the quotient property of logarithms?

The quotient property states that $$\log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n)$$ .

What is the power property of logarithms?

The power property states that $$\log_b(m^n) = n\log_b(m)$$ .

How do you convert a logarithmic equation to an exponential equation?

To convert $$\log_b(a) = c$$ to exponential form, write it as $$b^c = a$$ .

What is the value of $$\log_3(27)$$ ?

The value is 3, since $$3^3 = 27$$ .

What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a certain value. In $$\log_b(a)$$ , b is the base.

What is the significance of the logarithm of 1?

The logarithm of 1 in any base is always 0, since $$b^0 = 1$$ for any base b.

What is the significance of the logarithm of the base itself?

The logarithm of the base in any base is always 1, since $$b^1 = b$$ .

Logarithms and Exponentials Test Review 23-24 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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2.

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Since the logarithms are equal, set the arguments equal to each other: 4x - 5 = 2x - 1. Solving gives x = 2.

3.

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4.

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