UNIT 6- OBJECTIVE 5 - NATURAL LOGARITHMS

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The second Key on your calculator is the natural log key or ln which is
log, base e
(e is an irrational number equal to approximately 2.718).  Natural logs are
written ln250 and means loge250=5.52

Example 1
Find the natural logarithms to 4 decimal places.
a) ln(9.25)= 2.2246
b) ln(12.05)= 2.4891
c) ln(0.013)= -4.3428
d) ln(.5)= -.6931

On your calculator, you can also "undo" the ln function.  "Undoing" a ln is
called "finding the antilog".

If you were given ln(x) = 1.3 then x = inverse natural log of 1.3 or the natural
antilog of 1.3 or
x = e1.3=3.669

You should be able to get natural antilogs or inverse natural logs using
2nd ln or inv ln or ex key.

Example 2
Find the natural antilog to 4 decimal places.

a) ln(x)= -3.5
x= .0302

b) ln(x)= .09
x= 1.094

c) ln(x)= 4.75
x= 115.58

d) ln(x)= -.22
x= .8025

Logs to other bases: Your calculator will evaluate common logs (base 10)
and natural logs (base e).

For other bases, use on of the following conversions.

logbx = (logax)/(logab) = ln(x)/ln(b)

Example 3
log8250

Method 1: Rewrite using comon logs and evaluate.
log8250 = (log 250)/(log 8) = 2.655

Method 2: Rewrite using natural logs and evaluate.
log8250 = (ln 250)/(ln 8) = 2.655