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

Question

Which of the following uses the properties of logarithms to correctly evaluate log1023
?(1 point)
Responses

log1023=23
logarithm 10 superscript 23 baseline equals 23

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

log1023=1023
logarithm 10 superscript 23 baseline equals 10 superscript 23 baseline

log1023=10−23

GPT-4o mini · Answer

To evaluate $ \log_{10} 23 $, we should recall the basic properties of logarithms. Specifically, $ \log_{b} a $ gives us the exponent to which the base $ b $ must be raised to obtain $ a $. In this case, we are looking for $ x $ in the equation $ 10^x = 23 $. The logarithmic expression $ \log_{10} 23 $ represents this $ x $, which is not equal to any of the options given (such as 23, -23, $ 10^{23} $, or $ 10^{-23} $) under normal evaluations. Thus, none of the provided options correctly evaluate $ \log_{10} 23 $. However, we can summarize each response: 1. $ \log_{10} 23 = 23 $ - Not correct; that would imply $ 10^{23} = 23 $. 2. $ \log_{10} 23 = -23 $ - Not correct; that would imply $ 10^{-23} = 23 $. 3. $ \log_{10} 23 = 10^{23} $ - Not correct; that would imply $ 10^{10^{23}} = 23 $. 4. $ \log_{10} 23 = 10^{-23} $ - Not correct; that would imply $ 10^{10^{-23}} = 23 $. In conclusion, none of the provided answers accurately evaluates $ \log_{10} 23 $. The correct answer is that $ \log_{10} 23 $ is some value (approximately 1.362) that cannot be expressed in the provided options.