Question: What is the base of the logarithm if log_3(81) = 4?
Options:
3
4
9
81
Correct Answer: 3
Solution:
Since 81 is 3^4, the base of the logarithm is 3.
What is the base of the logarithm if log_3(81) = 4?
Practice Questions
Q1
What is the base of the logarithm if log_3(81) = 4?
3
4
9
81
Questions & Step-by-Step Solutions
What is the base of the logarithm if log_3(81) = 4?
Step 1: Understand that log_3(81) means 'to what power must 3 be raised to get 81'.
Step 2: Recognize that 81 can be expressed as a power of 3.
Step 3: Calculate 3 raised to the power of 4, which is 3^4 = 81.
Step 4: Since 3^4 equals 81, we confirm that the base of the logarithm is 3.
Logarithms – Logarithms are the inverse operations of exponentiation, indicating the power to which a base must be raised to obtain a certain number.
Exponential Relationships – Understanding the relationship between exponents and logarithms is crucial for solving logarithmic equations.
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