Algebra Know-It-ALL

Taking the natural logarithm of each side, we get

ln (ex)= ln 1,000,000

x= ln 1,000,000

This simplifies to a matter of finding a natural logarithm with a calculator. Rounded off to two decimal

places, we have

ln 1,000,000 ≈ 13.82

In the second case, we must solve the following equation for x:

ex= 0.0001

Taking the natural logarithm of each side, we get

ln (ex)= ln 0.0001

x= ln 0.0001

This simplifies, as in the first case, to a matter of finding a natural logarithm with a calculator. When we

do that, and then round off to two decimal places, we get

ln 0.0001 ≈ −9.21

Practice Exercises

This is an open-book quiz. You may (and should) refer to the text as you solve these problems.

Don’t hurry! You’ll find worked-out answers in App. C. The solutions in the appendix may

not represent the only way a problem can be figured out. If you think you can solve a particu-

lar problem in a quicker or better way than you see there, by all means try it!

Table 29-1. Comparison of exponentials for bases 1, 2, e, and 10. Values for base e

are approximate except for e^0 , which is exactly 1.

x 1 x^2 x^ ex^10 x

− 4 1 0.0625 0.0183 0.0001

− 3 1 0.125 0.0498 0.001

− 2 1 0.25 0.1353 0.01

− 1 1 0.5 0.3679 0.1

0 1 1 1 1

1 1 2 2.7183 10

2 1 4 7.3891 100

3 1 8 20.0855 1,000

4 1 16 54.5982 10,000

496 Logarithms and Exponentials