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Solution 3.3:6a

From Förberedande kurs i matematik 1

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Revision as of 09:25, 26 September 2008

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


3log34=4


Now, take the natural logarithm of both sides,


ln3log34=ln4


Using the logarithm law, lgab=blga, the left-hand side can be written as \displaystyle \log _{3}4\centerdot \ln 3 and the relation is


\displaystyle \log _{3}4\centerdot \ln 3=\ln 4


Thus, after dividing by \displaystyle \text{ln 3}, we have


\displaystyle \log _{3}4=\frac{\ln 4}{\ln 3}=\frac{1.386294...}{1.098612...}=1.2618595


which gives 1.262 as the rounded-off answer.

NOTE: on a calculator, the answer is obtained by pressing the buttons


\displaystyle \left[ 4 \right]\quad \left[ \text{LN} \right]\quad \left[ \div \right]\quad \left[ 3 \right]\quad \left[ \text{LN} \right]\quad \left[ = \right]

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