Question

Which uses the properties of logarithms to correctly evaluate log 10^23

Log 10^23 =1 23
Log 10^23 =10^-23
Log 10^23=-23
Log 10^23 =10^23

Answer 1

To evaluate \( \log 10^{23} \) using the properties of logarithms, we can use the power rule of logarithms, which states that \( \log_b(a^n) = n \cdot \log_b(a) \).

In this case, we are dealing with base 10:

\[
\log_{10}(10^{23}) = 23 \cdot \log_{10}(10).
\]

Since \( \log_{10}(10) = 1 \), we have:

\[
\log_{10}(10^{23}) = 23 \cdot 1 = 23.
\]

Thus, the correct evaluation is:

\[
\log 10^{23} = 23.
\]

From your options, the correct answer is:

**Log 10^23 = 23.**

(Note: There seems to be a typo in your option list; it should say "Log 10^23 = 23" instead of "Log 10^23 = 1 23").