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