Review: Log & Exponential Functions & Graphs

Front

What is the definition of a logarithm?

Back

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.

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the relationship between logarithmic and exponential functions?

Back

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

Front

What is the value of log_25(5)?

Back

1/2

Front

What is the value of log_3(9)?

Back

2

Front

What does the graph of a logarithmic function look like?

Back

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

Front

What is an asymptote in the context of logarithmic functions?

Back

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

Front

How do you convert an exponential equation to logarithmic form?

Back

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

Front

What is the value of log_5(125)?

Back

3

Front

What is the base of a logarithm?

Back

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.