Solving Logarithms Using a Calculator with Change of Base Property
Description/Explanation/Highlights
Video Description
This video explains how to use a calculator with the change of base property to find the value of any logarithm.
Steps and Key Points to Remember
To use a calculator and the change of base property to find the value of any logarithm, follow these steps:
- The log key on a calculator is a common log key which is base 10.
- To find the value of a common log (base 10) such as \(\log(43)\), simply press the log key, type in the number (in this example, 43) and press enter. The result is the value of the log. In this example, the log of 43 is approximately 1.6335 which means that \(10^{1.6335}\) is approximately 43.
- Finding the value of a log in another base cannot be done directly in most calculators but can easily be done using the change of base property.
- The change of base property states that you can find the value of any log by dividing the log of the argument by the log of the base using any base log you choose as long as both are the same. To use a calculator, we use base 10 (the common log) since we have that key. For example to find \(\log_3(22)\) we would type log(22)/Log(3) into our calculator and enter it. The result of this calculation is approximately 2.81, meaning that \(3^{2.81}\) is approximately 22.
- We could have chosen any base to use with the change of base formula and the answer would have been the same. For example, in the previous example, we could have used \(\log_5(22)/\log_5(3)\) and the answer would have been correct but we couldn’t have put it in the calculator that way since there is no log base 5 key!
- Many calculators have an LN key which is a natural log key (\(\log_ex\)). As long as it is used for both logs in the change of base property, it works equally well! For example to use LN in the previous example, type in LN(22)/LN(3) and the answer is the same!
Here are some key points to keep in mind when entering logs in the calculator using the change of base property.
- The LOG key on the calculator is a base 10 (common log) and can only find the value of a common log directly.
- To find the value of a log of any base, use the common log with the change of base property and type the log of the argument divided by the log of the base.
- Always remember that when finding the value of a log, the more decimals you keep the more accurate the result will be. It is best to type the entire change of base property in the calculator at once for accuracy.
- If available, it is acceptable to use the LN key (base e log) in the change of base property. The answer will be the same as the common LOG.
- Remember, any base works with the change of base formula but to use a calculator, we must choose a base that has a key on the calculator.
Video Highlights
- 00:00 Introduction
- 00:11 \(\log(43)\) example of finding the value of a log using a calculator
- 01:20 \(\log_3(22)=x\) example of using the calculator with the change of base property to find the value of a logarithm.
- 03:15 \(\log_7(49)=x\) example of finding the value with a calculator.
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