A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, if $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

How do you solve $$\text{log}_b(n) = k$$ for n?

To solve $$\text{log}_b(n) = k$$ , rewrite it in exponential form: $$n = b^k$$ .

How do you evaluate $$\text{log}_3(81)$$ ?

Since $$81 = 3^4$$ , we have $$\text{log}_3(81) = 4$$ .

How do you evaluate $$\text{log}_3igg(\frac{1}{9}igg)$$ ?

Since $$\frac{1}{9} = 3^{-2}$$ , we have $$\text{log}_3igg(\frac{1}{9}igg) = -2$$ .

What is the first step in solving $$\text{log}_7(n) = \frac{2}{3}\text{log}_7(8)$$ ?

Multiply both sides by 3 to eliminate the fraction: $$3\text{log}_7(n) = 2\text{log}_7(8)$$ .

What is the solution to $$\text{log}_8(3x + 7) = \text{log}_8(7x + 4)$$ ?

Set the arguments equal: $$3x + 7 = 7x + 4$$ , then solve for $$x$$ .

What is the base of a logarithm?

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

What is the inverse relationship between exponentiation and logarithms?

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

What is a common logarithm?

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

What is a natural logarithm?

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

Solving Logarithmic Equations Flashcards

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