How do you convert $$\text{log}_b(x) = y$$ to exponential form?

The conversion is done by rewriting it as $$b^y = x$$ .

Solve the equation $$\text{log}_6(2x + 3) = 3$$ .

First, rewrite it as $$6^3 = 2x + 3$$ , then solve for $$x$$ to get $$x = 106.5$$ .

What does $$\text{log}_b(1) = 0$$ signify?

It signifies that any base raised to the power of 0 equals 1, i.e., $$b^0 = 1$$ .

Rewrite $$\text{log}_8(x) = 0$$ in exponential form.

$$8^0 = x$$ , which means $$x = 1$$ .

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

The value is always 1, since $$b^1 = b$$ .

If $$\text{log}_2(16) = x$$ , what is the value of $$x$$ ?

$$x = 4$$ , because $$2^4 = 16$$ .

What is the change of base formula for logarithms?

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

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

The value is $$n$$ , since $$b^n$$ is the argument of the logarithm.

Lesson: Rewriting Logarithmic Equations Flashcards

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1.

FLASHCARD QUESTION

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What is the definition of a logarithm?

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2.

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3.

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4.

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What is the base of a logarithm?

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5.

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6.

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What is the relationship between logarithms and exponents?

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