Question
Using numerical analysis and the Power Rule of Logarithms, logxk=klogx
, how can log(1100)
be rewritten?(1 point)
Responses
2log−10
2 logarithm negative 10
log−20
logarithm negative 20
10log−2
10 logarithm negative 2
−2log10
, how can log(1100)
be rewritten?(1 point)
Responses
2log−10
2 logarithm negative 10
log−20
logarithm negative 20
10log−2
10 logarithm negative 2
−2log10
Answers
Answered by
GPT-4o mini
To rewrite \( \log(1100) \) using logarithmic properties, we can start by breaking down \( 1100 \) into its prime factors:
\[ 1100 = 11 \times 100 = 11 \times 10^2. \]
Using the properties of logarithms, we can rewrite \( \log(1100) \) as follows:
\[
\log(1100) = \log(11 \times 10^2) = \log(11) + \log(10^2).
\]
Using the Power Rule of Logarithms \( \log(a^b) = b \log(a) \):
\[
\log(10^2) = 2 \log(10).
\]
Thus,
\[
\log(1100) = \log(11) + 2 \log(10).
\]
However, in the provided options, we need to ascertain if any of those forms can represent \( \log(1100) \). None of the options directly align with the logs from our calculations.
If we consider base 10 logarithm of each given choice more carefully, they also don't seem to provide the necessary decomposition for \( \log(1100) \).
Therefore, it's clear that there was a misunderstanding in coding down \( \log(1100) \). However, if trying to match it to any choice, we would say none are particularly representative unless a further step is provided to reduce it to numerical equivalents based on logs and numbers given.
If you have any additional context or details about how you want \( 1100 \) to be related to the given answers, let me know!
\[ 1100 = 11 \times 100 = 11 \times 10^2. \]
Using the properties of logarithms, we can rewrite \( \log(1100) \) as follows:
\[
\log(1100) = \log(11 \times 10^2) = \log(11) + \log(10^2).
\]
Using the Power Rule of Logarithms \( \log(a^b) = b \log(a) \):
\[
\log(10^2) = 2 \log(10).
\]
Thus,
\[
\log(1100) = \log(11) + 2 \log(10).
\]
However, in the provided options, we need to ascertain if any of those forms can represent \( \log(1100) \). None of the options directly align with the logs from our calculations.
If we consider base 10 logarithm of each given choice more carefully, they also don't seem to provide the necessary decomposition for \( \log(1100) \).
Therefore, it's clear that there was a misunderstanding in coding down \( \log(1100) \). However, if trying to match it to any choice, we would say none are particularly representative unless a further step is provided to reduce it to numerical equivalents based on logs and numbers given.
If you have any additional context or details about how you want \( 1100 \) to be related to the given answers, let me know!