Activities

Logarithms - meaning

Consider the exponential function y = 10x.

We define the logarithmic function y = log x  as the inverse function of y = 10x.

Consider the example 103 = 1000.

It also follows that:

Logarithm is another word for index.

Other bases are possible.

Consider the exponential function y = 5x.

We define the logarithmic function y = log5 x as the inverse function of y = 5x.

(The notation log without the subscript is taken to mean log10.)

Consider the example 54 = 625.


Index notation and log notation are two ways of writing the same information.

Problem - What is the value of log168 ?

The index law  a0 = 1  has its equivalent in log notation.

For the other index laws, what are the equivalents in log notation?

The graphs of a function and its inverse are reflections of each other in the line y=x.

Consider the graphs of y = 10x and y = log x.

Why does the domain of y = log x exclude 0 and all the negative numbers?

Exploremath activity

  • Experiment with the log function by changing the base.
  • View the corresponding exponential function as a reflection in the line y = x.

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