Intermediate Algebra (11th edition)

A calculator key labeled is used to evaluate natural logarithms. Consult

your calculator manual to see how to use this key.

ln x

SECTION 10.5 Common and Natural Logarithms 607

x

y

02468

2

–2

y = ln x

FIGURE 15

Evaluating Natural Logarithms

Using a calculator, evaluate each logarithm to four deci-

mal places.

(a)

As with common logarithms, a number between 0

and 1 has a negative natural logarithm.

(b) (c)

See FIGURE 16.

NOW TRY

ln 192.7L5.2611 ln 10.84L2.3832

ln 0.5841L-0.5377

EXAMPLE 5

FIGURE 16

NOW TRY
EXERCISE 5
Using a calculator, evaluate
each logarithm to four
decimal places.

(a)ln 0.26 (b)ln 12

(c)ln 150

NOW TRY ANSWERS

(a) (b)2.4849
(c)5.0106

1.3471

OBJECTIVE 4 Use natural logarithms in applications.

Applying a Natural Logarithmic Function

The altitude in meters that corresponds to an atmospheric pressure of xmillibars is

given by the logarithmic function defined by

(Source:Miller, A. and J. Thompson, Elements of Meteorology, Fourth Edition,

Charles E. Merrill Publishing Company.) Use this function to find the altitude when

atmospheric pressure is 400 millibars. Round to the nearest hundred.

Let and substitute in the expression for

Let Use a calculator.

Atmospheric pressure is 400 millibars at approximately 6900 m. NOW TRY

ƒ 14002 L 6900

ƒ 14002 = 51,600-7457 ln 400 x=400.

x= 400 ƒ 1 x 2.

ƒ 1 x 2 =51,600- 7457 ln x.

EXAMPLE 6

NOTE In Example 6,the final answer was obtained using a calculator without

rounding the intermediate values. In general, it is best to wait until the final step to

round the answer. Round-offs in intermediate steps can lead to a buildup of round-off

error, which may cause the final answer to have an incorrect final decimal place digit

or digits.

NOW TRY
EXERCISE 6
Use the logarithmic function
in Example 6to approximate
the altitude when atmospheric
pressure is 600 millibars.
Round to the nearest hundred.

approximately 3900 m