Logarithms – Change of Base | Don't Memorise | Summary and Q&A

TL;DR
The change of base formula allows us to find logarithm values using different bases, such as base 10 or base e.
Key Insights
- 😀 Logarithms with bases 10 and e are commonly used in scientific and financial calculations.
- ⚾ The change of base formula allows us to find logarithm values with different bases by using the formula log of a to the base B can be written as log of a to the base x divided by log of B to the base x.
- ⚾ The change of base formula can be used when calculators do not have a specific logarithm function, such as log to the base 3.
- ⚾ The change of base formula can be used with bases e or 10, depending on the available functions in the calculator.
- ⚾ The result of logarithm calculations using the change of base formula should be the same, regardless of the base used, as they represent the same logarithmic value.
- ⚾ The change of base formula can be used to derive the property that log of a to the base B multiplied by log of B to the base a will always equal one.
Transcript
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Questions & Answers
Q: What are the most commonly used bases in logarithms?
The most commonly used bases in logarithms are base 10 and base e (also known as the natural logarithm).
Q: How does the change of base formula work?
The change of base formula allows us to find logarithm values using different bases. It states that log of a to the base B can be written as log of a to the base x divided by log of B to the base x.
Q: How can we calculate log 8 to the base 3 using a calculator?
Since most calculators have logarithm functions for base 10 and base e, we can use the change of base formula by writing log 8 to the base 3 as log 8 to the base e divided by log 3 to the base e.
Q: What if the calculator does not have a natural logarithm function?
If the calculator does not have a natural logarithm function, we can also use the change of base formula with base 10. In this case, log 8 to the base 3 can be written as log 8 to the base 10 divided by log 3 to the base 10.
Summary & Key Takeaways
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Logarithms with bases 10 and e are commonly used in scientific and financial calculations.
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The change of base formula states that log of a to the base B can be written as log of a to the base x over log of B to the base x.
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To calculate log 8 to the base 3, the change of base formula can be used with bases e or 10.