Solution 3.3:6a

From Förberedande kurs i matematik 1

The calculator does not have button for log3, but it does have one for the natural logarithm ln, so we need to rewrite log34 in terms of ln.

If we go back to the definition of the logarithm, we see that log34 is that number which satisfies

Now, take the natural logarithm of both sides,

Using the logarithm law, lgab=blga, the left-hand side can be written as log34ln3 and the relation is

log34ln3=ln4.

Thus, after dividing by ln3, we have

which gives 1.262 as the rounded-off answer.

Note: On the calculator, the answer is obtained by pressing the buttons