# How to find logarithms on ti-89

### The logarithm

Representation of positive numbers as powers

Fig. 7590 The graph for the function y = 2 ^ x (SVG)

Your table will confirm by way of example:

"Every" positive number can be represented as a power with the base 2.

Think for a moment what you would get if instead of the graph of the graph of would have taken as a basis. For the same -Values of the above table results in the following table

Fig. 7682 The graph for the function y = 10 ^ x (SVG)

and the graph in Figure 7682, so that we can also formulate here:

"Every" positive number can be represented as a power with a base of 10.

From the graph of the Function one would deduce accordingly:

"Every" positive number can be represented as a power with the base ......

More generally applies to any base , With :

Definition of the logarithm for base 2

In the previous section we saw that any positive real number can be represented as a power to a given basis. This power representation is the foundation for defining (and understanding) the logarithm. If one takes base 2 as a basis, one finds (see table):

In words:

In words:

These exponents of powers to base 2 are the logarithms to base 2 or logarithms of 2. In relation to the above examples, one formulates:

If you formulate these examples in general, you get the following definition:

In the graphic representation of the logarithm appears as the abscissa value, as can be seen in Figure 7683.

Fig. 7683 The logarithm as an abscissa value (SVG)

Exercise:

Logarithms with arbitrary bases

In the section "Definition of the logarithm for base 2" we introduced the logarithm for base 2. We have assumed that positive numbers are represented as powers to base 2. We want to briefly show the appropriate way if you have base 10 or is based on. Our goal will be to arrive at a general logarithm definition. In the section "Representation of positive numbers as powers" we found:

In words:

In words:

Or according to the definition of the logarithm for base 2:

We can already record essential findings:

- The exponents of a power representation are called logarithms
- There is no such thing as an absolute logarithm, because the value of the logarithm depends on the underlying basis!

Nothing stands in the way of a general logarithm definition:

a) so .................

b) so .................

c) so .................

d) so .................

e) so .................

f) so .................

Fig. 7684 the general logarithm (SVG)

Every logarithm is - as we now know - connected to a base. The general -Logarithm is rarely used in arithmetic practice. For the two most important logarithms, we are introducing a new, less cumbersome notation in which the base is no longer explicitly noted.

The natural logarithm

The decadic logarithm

The decadic logarithm or 10's logarithm has a base of 10 and becomes with abbreviated:

The decadic logarithm will be of great importance in the accompanying text "The logarithmic paper".

The decadic logarithm will be of great importance in the accompanying text "The logarithmic paper".

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