Property: Quotient Rule of Logarithms

$$\text{log}_bigg(\frac{m}{n}igg) = \text{log}_b(m) - \text{log}_b(n)$$

Property: Power Rule of Logarithms

$$\text{log}_b(m^k) = k \times \text{log}_b(m)$$

Definition: Exponential Function

A function of the form $$f(x) = a \times b^x$$ where a is a constant, b is the base, and x is the exponent.

Definition: Base of a Logarithm

The base of a logarithm is the number that is raised to a power to obtain a given number.

Example: Change of Base Formula

$$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any base k.

Definition: Natural Logarithm

The natural logarithm is the logarithm to the base e, denoted as $$\text{ln}(x)$$ .

Logs & Exponentials Properties and Equations Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Evaluate the following logarithm: log₃27

Back

3

2.

FLASHCARD QUESTION

Front

Solve for x: log₆x + log₆(x-5) = 2

Back

9

3.

FLASHCARD QUESTION

Front

Back

3logm - logn

4.

FLASHCARD QUESTION

Front

Logarithmic functions are the inverse of...

Back

Exponential Functions

5.

FLASHCARD QUESTION

Front

Back

logx - logy

6.

FLASHCARD QUESTION

Front

Definition: Logarithm

Back

The logarithm of a number is the exponent to which the base must be raised to produce that number.

7.

FLASHCARD QUESTION

Front

Property: Product Rule of Logarithms

Back

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