Question

Which of the following uses the properties of logarithms to correctly evaluate  log1023 ?(1 point)Responseslog1023=−23logarithm 10 superscript 23 baseline equals negative 23log1023=10−23logarithm 10 superscript 23 baseline equals 10 superscript negative 23 baselinelog1023=23logarithm 10 superscript 23 baseline equals 23log1023=1023

Answer 1

To evaluate \( \log_{10} 23 \) using properties of logarithms, let’s clarify the options you’ve provided.

The correct approach to evaluate \( \log_{10} 23 \) directly from the choices would not work, as you typically cannot determine the logarithm of a number without a calculator or table. However, let's analyze the options mentioned:

1. \( \log_{10} 23 = -23 \) - This is incorrect. Logarithms of positive numbers cannot be negative if the base is also positive.

2. \( \log_{10} 23 = 10^{-23} \) - This is incorrect. The logarithm represents an exponent and cannot equal a number in this manner.

3. \( \log_{10} 23 = 23 \) - This is incorrect as \( 10^{23} \) is a very large number significantly greater than 23.

4. \( \log_{10} 23 = 10^{23} \) - This is incorrect as well.

None of these options correctly evaluate \( \log_{10} 23 \). The actual value of \( \log_{10} 23 \) is a positive number, roughly equal to 1.362.

If these options are all there is, it appears that none of them are correct.

If you have further text or additional context regarding the evaluation, please share!