Logarithms Using a Calculator
Logarithms using a calculator
Calculating a logarithmic value
There are many different types and models of scientific calculators. It is very important to be familiar with your own calculator and the different function buttons. Some calculators only have two buttons for logarithms: one for calculating the common logarithm (base is equal to \(\text{10}\)) and another for calculating the natural log (base is equal to \(e\)). Newer models will have a third button which allows the user to calculate the logarithm of a number to a certain base.
Example
Question
Use a calculator to determine the following values (correct to \(\text{3}\) decimal places):
- \(\log{9}\)
- \(\log{\text{0.3}}\)
- \(\log{\cfrac{3}{4}}\)
- \(\log{(-2)}\)
Use the common logarithm function on your calculator
Make sure that you are familiar with the “LOG” function on your calculator. Notice that the base for each of the logarithms given above is \(\text{10}\).
Write the final answer
- \(\log{9} = \text{0.954}\)
- \(\log{\text{0.3}} = -\text{0.523}\)
- \(\log{\cfrac{3}{4}} = -\text{0.125}\)
- \(\log{(-2)} =\) undefined
Example
Question
Use a calculator to determine the following values (correct to \(\text{3}\) decimal places):
- \(\log{x} = \text{1.7}\)
- \(\log{t} = \cfrac{2}{7}\)
- \(\log{y} = -\text{3}\)
Use the second function and common logarithm function on your calculator
For each of the logarithms given above we need to calculate the inverse of the logarithm (sometimes called the antilog). Make sure that you are familiar with the “\(\text{2}\)nd F” button on your calculator.
Notice that by pressing the “\(\text{2}\)nd F” button and then the “LOG” button, we are using the “\(10^{x}\)” function on the calculator, which is correct since exponentials are the inverse of logarithms.
Write the final answer
- \(x = \text{50.119}\)
- \(t = \text{1.930}\)
- \(y = \text{0.001}\)
Example
Question
Use a calculator to find \(\log_{2}{5}\) correct to two decimal places.
Solution
Use a change of base to convert given logarithm to base \(\text{10}\)
\[\log_{2}{5} = \cfrac{\log{5}}{\log{2}}\]Use the common logarithm function on your calculator
Write the final answer
\[\log_{2}{5} = \text{2.32}\]Important:
-
Do not write down an intermediate step when doing this type of calculation:
\begin{align*} \log_{2}{5} &= \cfrac{\log{5}}{\log{2}} \\ &= \cfrac{\text{0.7}}{\text{0.3}} \quad (\text{this step can cause rounding off errors}) \\ &= \text{2.33} \end{align*}Perform the calculation in one step on your calculator:
\begin{align*} \log_{2}{5} &= \cfrac{\log{5}}{\log{2}} \\ &= \text{2.32} \end{align*} -
Do not round off before the final answer as this can affect the accuracy of the answer.
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Be sure that you determine the correct sequence and order of operations when using a calculator.
This lesson is part of:
Functions III