Algebra Know-It-ALL

Part Three 539

The common log is sometimes called the base-10 log, because 10 is the base that we raise to
various powers.

Question 29-2

According to the definition in Answer 29-1, what is the common log of 10? Of 100? Of
1,000? Of 10,000? What happens to the common log of a positive number, as that number
grows larger and larger indefinitely?

Answer 29-2

The common log is related to a growing positive number like this:

• The common log of 10 is 1, because 10^1 = 10.


• The common log of 100 is 2, because 10^2 = 100.

Table 30-5. Selected values for graphing the functions

y=x^3 + 3 x^2 + 3 x+ 1 and y=x^3 + 6 x^2 + 12 x+ 8.

This system has no real solutions.

xx^3 + 3 x^2 + 3 x+ 1 x^3 + 6 x^2 + 12 x+ 8

− 5 − 64 − 27

− 4 − 27 − 8

− 3 − 8 − 1

− 2 −1 0

−1 0 1

0 1 8

1 8 27

2 27 64

x

y

No

intersection

points

No

real

solutions

Figure 30-11 Illustration for Answer 28-10.

The first function is graphed

as a solid curve; the second

function is graphed as a dashed

curve. The curves do not

intersect (although they come

close!), so there are no real

solutions. On the x axis, each

increment is 1 unit. On the

y axis, each increment is 10

units.