# Logarithmic Functions

## Vocabulary

### asymptote

line that a graph approaches as one of the variables approaches infinity or negative infinity

### change of base rule

rule that states that a logarithm of a number in base $b$ can be changed to base $a$ by dividing the logarithm of the number in base $a$ by the logarithm of $b$ in base $a$

### common logarithm

logarithm with base 10, or the exponent to which 10 is raised to equal a given number; written as $\log{x}$, where $x$ is the given number

### exponent

number that indicates how many times a base is multiplied by itself and shown by a raised number, such as $4^{3}$

### input

value in the domain of a function

### inverse function

result of switching the inputs and outputs of a function when the result is also a function. The composition of a function and its inverse is the identity function.

### logarithm

exponent $x$ to which a base $b$ is raised to produce a given number $y$, written as:
$x=\log_b{y}$

### logarithmic function

function, where $b>0$ and $b\neq 1$, written in the form:
$f(x)=\log_b{x}$

### natural logarithm

logarithm with base $e$, where $e\approx2.718281845\dots$, or the exponent to which $e$ must be raised to equal a given number; written as $\ln{x}$, where $x$ is the given number

### output

value in the range of a function

### parent function

function of a certain type that has the simplest algebraic rule

### power rule of logarithms

rule that states that the logarithm of a power is equal to the product of the exponent and the logarithm of the base

### product rule of logarithms

rule that states that the logarithm of a product is equal to the sum of the logarithms of the factors

### quotient rule of logarithms

rule that states that the logarithm of a quotient is equal to the difference of the logarithm of the dividend and the logarithm of the divisor