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) only use answers ive given

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 can use the definition of the logarithm. The logarithm $ \log_{10} 23 $ represents the exponent to which the base (10) must be raised to produce the number 23. The possible responses you've given don't correctly evaluate $ \log_{10} 23 $ based on the properties of logarithms. Here's what each option states: 1. $ \log_{10} 23 = 23 $: This is incorrect. $ 10^{23} $ is much larger than 23. 2. $ \log_{10} 23 = -23 $: This is also incorrect. A logarithm cannot be negative if the argument (23) is greater than 1. 3. $ \log_{10} 23 = 1023 $: This is incorrect. This implies $ 10^{1023} $ which is vastly larger than 23. 4. $ \log_{10} 23 = 10^{-23} $: This implies that $ 10^{-23} $ equals 23, which is not true. None of the options you provided correctly evaluate $ \log_{10} 23 $. The correct value can be approximated using a calculator, but based on the choices given, there’s no valid response. A correct evaluation would yield a value that is between 1 and 2 since $ 10^1 = 10 $ and $ 10^2 = 100$, and 23 lies between these two powers. Thus, the answer is that none of the provided statements accurately represent $ \log_{10} 23$.