Which of the following uses the properties of logarithms to correctly evaluate log1023

Question

?(1 point)
Responses

log1023=23
logarithm 10 superscript 23 baseline equals 23

log1023=−23
logarithm 10 superscript 23 baseline equals negative 23

log1023=10−23
logarithm 10 superscript 23 baseline equals 10 superscript negative 23 baseline

log1023=1023

Answer 1

To evaluate \( \log_{10}(23) \), we can use the properties of logarithms. However, we need to clarify a misunderstanding in the responses provided.

The expression \( \log_{10}(23) \) is not equal to any of the options given (23, -23, \( 10^{-23} \), or \( 10^{23} \)). The logarithm \( \log_{10}(23) \) actually represents the exponent to which 10 must be raised to obtain the value 23.

So, it is incorrect to state that:

1. \( \log_{10}(23) = 23 \)
2. \( \log_{10}(23) = -23 \)
3. \( \log_{10}(23) = 10^{-23} \)
4. \( \log_{10}(23) = 10^{23} \)

None of these statements are correct because they misinterpret the properties of logarithms.

The value \( \log_{10}(23) \) is approximately 1.3617, which is not represented in any of the provided answers.

Please ensure all logarithmic evaluations consider the definition and properties of logarithms correctly.