Review: Log & Exponential Functions & Graphs

A logarithm is the exponent to which a base must be raised to produce a given number. For example, in the expression log_b(a) = c, b^c = a.

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Logarithmic functions are the inverses of exponential functions. If y = b^x, then x = log_b(y).

1/2

2

The graph of a logarithmic function is a curve that increases slowly and approaches the vertical line (asymptote) at x=0.

An asymptote is a line that a graph approaches but never touches. For logarithmic functions, the vertical asymptote is typically at x=0.

To convert an exponential equation a^b = c to logarithmic form, write it as log_a(c) = b.

3

The base of a logarithm is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.