Proof: log a + log b = log ab | Logarithms | Algebra II | Khan Academy
Khan Academy・5 minutes read
Logarithm properties are derived from the relationship between exponents and logarithms, with expressions like log base x of a resulting in an exponent where x to the n equals a, and playing with different values helps discover these properties. Knowing that logarithms are akin to exponents aids in comprehending and utilizing logarithm properties efficiently.
Insights
- Logarithm properties are derived from the connection between exponents and logarithms, where log base x of a results in an exponent, x to the n equals a.
- Experimenting with various values for x, l, m, a, and b can unveil logarithm properties, such as the equation log base x of a times b equals log base x of a plus log base x of b, all rooted in the relationship between exponents and logarithms.
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Recent questions
What are logarithm properties?
Logarithm properties are rules based on the relationship between exponents and logarithms.
How do you evaluate a logarithm expression?
To evaluate a logarithm expression like log base x of a, find the exponent where x to the n equals a.
How can logarithm properties be discovered?
By experimenting with different values for x, l, m, a, and b, logarithm properties can be uncovered.
What is the property of log base x of a times b?
The property that log base x of a times b equals log base x of a plus log base x of b is derived from the relationship between exponents and logarithms.
How can understanding logarithms as exponents be helpful?
Understanding that logarithms are essentially exponents aids in comprehending and effectively applying logarithm properties.
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Summary
00:00
Relationship between exponents and logarithms explained
- Logarithm properties are based on the relationship between exponents and logarithms.
- Evaluating a logarithm expression like log base x of a results in an exponent, where x to the n equals a.
- By playing around with different values for x, l, m, a, and b, logarithm properties can be discovered.
- The property that log base x of a times b equals log base x of a plus log base x of b is derived from the relationship between exponents and logarithms.
- Understanding that logarithms are essentially exponents helps in grasping and applying logarithm properties effectively.
