Logarithmic functions 'undo' exponential functions. The input of one is the output of the other.

Output values change multiplicatively as input values change additively.

Output values change additively as input values change multiplicatively.

It results in the graph of its inverse, a logarithmic function.

Rapid increase as $x$ increases (if $b > 1$), vertical asymptote at $x=0$, no horizontal asymptote.

Slow increase as $x$ increases (if $b > 1$), horizontal asymptote at $y=0$, no vertical asymptote.

The domain of an exponential function is the range of its inverse logarithmic function, and vice versa.

It acts as a 'mirror' across which the graphs of the function and its inverse are reflected.

Swap $x$ and $y$ to get $x = b^y$, then solve for $y$ to get $y = \log_b(x)$.

Swap the $x$ and $y$ coordinates.

Reflect the graph of $y = b^x$ over the line $y = x$.

A function of the form $f(x) = a \log_b(x)$, where $b > 0$ and $b \neq 1$, and $a \neq 0$.

A function of the form $f(x) = ab^x$, where $a$ is the coefficient and $b$ is the base.

The value $b$ in $\log_b(x)$, where $b > 0$ and $b \neq 1$.

The value $a$ in $f(x) = ab^x$.

The input value $x$ in $\log_b(x)$.

The function $h(x) = x$, a straight line with a slope of 1 passing through the origin.

A logarithmic function with the same base.

A transformation where the x and y coordinates of a point are swapped.

A horizontal line that a graph approaches as $x$ tends to $+\infty$ or $-\infty$.

A vertical line that a graph approaches as $x$ approaches a certain value.