Algebra Applications: Logarithmic Functions

Algebra Applications: Logarithmic Functions

[Music]

[Music]

[Music]

Title: Algebra Applications: Logarithmic Functions

Title: An Introduction to Logarithms

Narrator: You've seen how exponential functions are

ideal for modeling phenomena that change in value in

huge leaps.

The graph of earthquake intensity is an

exponential function.

The inverse of an exponential function is a

logarithmic function.

The graphs of exponential and logarithmic functions are

mirror images of each other along the graph of Y equals x.

Logarithmic functions are ideal for measuring phenomena

that are exponential in nature.

In the case of earthquakes, rather than intensity, which

is an unwieldy number, an earthquakes magnitude is

measured, and magnitude is a logarithmic measure.

In this program we will explore two applications of

logarithmic functions.

In the first segment sound intensity, measured

logarithmically as decibels, is explored.

In particular, the risk of prolonged exposure to loud

sounds can result in hearing loss.

We look at the mathematics of hearing loss.

In the second example we return to earthquakes, but in

this case underwater earthquakes, which give rise

to tsunamis.

We look at how earthquake magnitude is measured and

analyze ways of creating more manageable graphs using a

logarithmic scale.