Question

evaluate logarithms (level 2) unique id: 0298
this is the only question in this section.
question
what is the value of \\(\log \frac{1}{10}\\)?
answer attempt 8 out of 10

Explanation:

Step1: Recall the logarithm property

We know that for a logarithm with base \( b \) (here \( b = 10 \), since it's a common logarithm, \( \log \) means \( \log_{10} \)), and \( \frac{1}{10}=10^{- 1} \). The logarithm property is \( \log_{b}b^{x}=x \).

Step2: Apply the property

Given \( \log_{10}\frac{1}{10}=\log_{10}10^{-1} \). By the property \( \log_{b}b^{x}=x \), when \( b = 10 \) and \( x=-1 \), we get \( \log_{10}10^{-1}=-1 \).

Answer:

\(-1\)