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

Question

GPT-4o mini · Answer

To evaluate $\log_{10}(23)$, we should remember the basic property of logarithms: 1. $\log_{b}(b) = 1$ for any base $b$, 2. $\log_{b}(1) = 0$ for any base $b$, 3. $\log_{b}(a \cdot c) = \log_{b}(a) + \log_{b}(c)$, 4. $\log_{b}(a/c) = \log_{b}(a) - \log_{b}(c)$, 5. $\log_{b}(a^n) = n \cdot \log_{b}(a)$. None of the given options correctly apply the logarithmic properties to evaluate $\log_{10}(23)$. In fact, $\log_{10}(23)$ is simply a specific value that does not simplify nicely to any of the options given. Therefore, none of the responses (such as $-23$, $10^{-23}$, $23$, or $1023$) correctly evaluate $\log_{10}(23)$. If you were looking to calculate or approximate $\log_{10}(23)$, it would usually be done using a calculator, yielding approximately $1.362$.