Flashcard 10 - Logarithmic Functions

The parent function of logarithmic functions is $$y = \text{log}_b(x)$$ , where $$b > 0$$ and @@b eq 1@@.

It represents a horizontal shift of the graph of $$y = \text{log}_3(x)$$ to the left by 5 units.

The inverse is $$f^{-1}(x) = 3^x$$ .

In logarithmic form, it is written as $$\text{log}_3(81) = 4$$ .

This represents a horizontal shift to the right by 1 unit and a vertical shift up by 4 units.

The domain is $$x > 0$$ .

The range is all real numbers, or $$(-\text{∞}, \text{∞})$$ .

The base of a logarithm is the number that is raised to a power to obtain a given value, denoted as $$b$$ in $$y = \text{log}_b(x)$$ .

The graph passes through the point (1,0), approaches the vertical line $$x=0$$ , and increases without bound as $$x$$ increases.

Logarithmic functions are the inverses of exponential functions.