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# 11 Natural logarithms and powers of e on your calculator

Natural logarithms, for example , can be evaluated on your calculator using the key. The second function of this key () permits the calculation of powers of . Note that an approximate value for itself can be obtained using the key sequence ().

Remember that means the same as ln. Some calculators have a key instead of .

## Activity 20 Calculating natural logarithms and powers of e

Calculate the value of each of the following using your calculator, giving each answer to 3 significant figures.

### Answer

1. (to 3 significant figures).
2. (to 3 significant figures).
3. (to 3 significant figures).

   Notice that this is about three times the answer to part (2). In fact, the exact value of is precisely three times the exact value of . This is because , and for any base of logarithm, . This is an important result for logarithms. In this case we have .

4. (to 3 significant figures).

   To calculate this answer correctly, you need to remember to close the bracket after the 3 on your calculator display.

5. (to 3 significant figures).

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