UNIT 6- OBJECTIVE 5 - NATURAL LOGARITHMS

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 log

_{e}250=5.52Example 1Find 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 = e

^{1.3}=3.669You should be able to get natural antilogs or inverse natural logs using 2nd ln or inv ln or e

^{x}key.

Example 2Find 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. log

_{b}x = (log_{a}x)/(log_{a}b) = ln(x)/ln(b)Example 3log_{8}250Method 1: Rewrite using comon logs and evaluate. log

_{8}250 = (log 250)/(log 8) = 2.655Method 2: Rewrite using natural logs and evaluate. log

_{8}250 = (ln 250)/(ln 8) = 2.655

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