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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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Description
Test your knowledge on basic logarithmic properties and values in this quiz. Questions include evaluating logarithms, understanding their bases, and exploring equivalent expressions. Perfect for students studying logarithms in mathematics.
