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Questions and Answers
What is the value of $ ext{log}_5 5$?
What is the value of $ ext{log}_5 5$?
- 5
- 1 (correct)
- 0
- 10
What is the base of the logarithm in $ ext{log}_5$?
What is the base of the logarithm in $ ext{log}_5$?
- 1
- 5 (correct)
- 2
- 10
Which expression is equivalent to $ ext{log}_5 25$?
Which expression is equivalent to $ ext{log}_5 25$?
- $ rac{1}{2}$
- $5^2$
- $ ext{log}_5 5^2$ (correct)
- $2 ext{log}_5 5$
What does $ ext{log}_5 1$ equal?
What does $ ext{log}_5 1$ equal?
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What is the relationship between $ ext{log}_5 125$ and the exponent required to express 125 as a power of 5?
What is the relationship between $ ext{log}_5 125$ and the exponent required to express 125 as a power of 5?
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Study Notes
Logarithm Basics
- The value of $log_5 5$ is 1. This is because 5 raised to the power of 1 equals 5.
- In the expression $log_5$, the base of the logarithm is 5. This means we are asking what power we need to raise 5 to in order to get the given number.
- The expression $log_5 25$ is equivalent to 2. This is because 5 raised to the power of 2 equals 25.
- The value of $log_5 1$ is 0. This is because any number raised to the power of 0 equals 1.
Logarithm and Exponents Relationship
- The relationship between $log_5 125$ and the exponent required to express 125 as a power of 5 is that they are inverse operations. $log_5 125$ equals 3, which is the same as the exponent required in the expression $5^3 = 125$.
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