The Exponent-Logarithm Relationship Quick Check

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Question
Use properties of exponents to find the value of log81
.(1 point)
Responses

18
Start Fraction 1 over 8 End Fraction

8
8

0
0

1
1

1 answer

To find the value of \( \log 81 \), we first need to understand that \( \log_a b = c \) means \( a^c = b \). However, the question does not specify a base for the logarithm (common base 10 or base \( e \)), so I will assume we are looking for the logarithm in base 10 or base \( e \) for the sake of explanation.

Since 81 can be expressed as \( 3^4 \): \[ \log 81 = \log (3^4) \]

Using the property of logarithms that states \( \log(a^b) = b \cdot \log(a) \), we can rewrite this as: \[ \log 81 = 4 \cdot \log 3 \]

Since the options provided in your quick check do not include a direct logarithmic evaluation, it's likely that it's expecting to evaluate this logarithm using its relationship in base (perhaps base 3).

If we take base 3: \[ \log_3 81 = \log_3 (3^4) = 4 \]

However, if you are finding \( \log_{10} 81 \), you will need to use either a calculator or logarithm tables, which would yield approximately 1.908:

Since the question options have numbers only and based on common logarithm properties and recognizing that \( 81 = 3^4 \): Among the provided responses, the correct answer for \( \log 81 \) if assuming evaluations likes \( \log_{3} \) is:

  • The closest logical choice of those would be 1 since that does not exceed normalized values that can be attributed through base adjustments (albeit, common only gets you near 2 via calculators).

Please ensure that the logarithm base is confirmed to provide an accurate answer if further or more refined selections are expected.