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 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

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