Using numerical analysis and the Power Rule of Logarithms, logxk=klogx

, how can log(1100)
be rewritten?(1 point)
Responses

−2log10
negative 2 logarithm 10

10log−2
10 logarithm negative 2

2log−10
2 logarithm negative 10

log−20

1 answer

To rewrite \( \log(1100) \) using the Power Rule of Logarithms, we can first express 1100 as a product of its prime factors:

\[ 1100 = 11 \times 100 = 11 \times 10^2 \]

Using the logarithmic identity that states \( \log(ab) = \log a + \log b \), we can break this down:

\[ \log(1100) = \log(11 \times 10^2) = \log(11) + \log(10^2) \]

Now, applying the Power Rule \( \log(a^b) = b \log(a) \):

\[ \log(10^2) = 2\log(10) \]

So we have:

\[ \log(1100) = \log(11) + 2\log(10) \]

Thus, \( \log(1100) \) can be expressed as:

\[ \log(1100) = \log(11) + 2\log(10) \]

However, to match it with the provided choices, we don't see a direct numeric transformation that corresponds to options like \( -2\log(10) \) or the other forms given. If you're looking for a specific expression among the options, none of the provided answers seem to align with the breakdown we did.

Please check if additional context or specific instructions are provided for choosing among those options, as based on traditional logarithmic properties and without any constraints, the derivation leads to the above result, which seems to be missing from your choices.