Question
Use the properties of logarithms to evaluate the expression.
log Subscript Baseline 10 squared
Question content area bottom
Part 1
log Subscript Baseline 10 squaredequals
enter your response here
(Simplify your answer.)
log Subscript Baseline 10 squared
Question content area bottom
Part 1
log Subscript Baseline 10 squaredequals
enter your response here
(Simplify your answer.)
Answers
Answered by
GPT-4o mini
To evaluate \( \log_{10} 2 \) using the properties of logarithms, we can express it in a simpler form.
The logarithm of the number 2 can be approximated or can be calculated using a calculator, but it doesn't simplify nicely into whole numbers without a specific calculation.
Assuming you meant \( \log_{10}(2^2) \), we can simplify it:
\[
\log_{10}(2^2) = 2 \cdot \log_{10}(2)
\]
To find \( \log_{10}(2) \), you would typically use a calculator, which gives approximately:
\[
\log_{10}(2) \approx 0.3010
\]
Therefore:
\[
\log_{10}(2^2) = 2 \cdot \log_{10}(2) \approx 2 \cdot 0.3010 = 0.6020
\]
If you meant \( \log_{10}(2) \) directly, as a function, it's simply \( \log_{10}(2) \).
If you need a final answer for \( \log_{10}(2^2) \), it's approximately \( 0.6020 \). Please clarify if you mean something different!
The logarithm of the number 2 can be approximated or can be calculated using a calculator, but it doesn't simplify nicely into whole numbers without a specific calculation.
Assuming you meant \( \log_{10}(2^2) \), we can simplify it:
\[
\log_{10}(2^2) = 2 \cdot \log_{10}(2)
\]
To find \( \log_{10}(2) \), you would typically use a calculator, which gives approximately:
\[
\log_{10}(2) \approx 0.3010
\]
Therefore:
\[
\log_{10}(2^2) = 2 \cdot \log_{10}(2) \approx 2 \cdot 0.3010 = 0.6020
\]
If you meant \( \log_{10}(2) \) directly, as a function, it's simply \( \log_{10}(2) \).
If you need a final answer for \( \log_{10}(2^2) \), it's approximately \( 0.6020 \). Please clarify if you mean something different!