Question

evaluate the expression without using a calculator.
\log _{10}\frac{1}{10}

\log _{10}\frac{1}{10}=\square

Explanation:

Step1: Recall log property

Recall that \(\log_{a}a^{x}=x\) and \(\frac{1}{a}=a^{-1}\). So, \(\frac{1}{10}=10^{-1}\).

Step2: Substitute into log

Substitute \(\frac{1}{10}=10^{-1}\) into \(\log_{10}\frac{1}{10}\), we get \(\log_{10}10^{-1}\).

Step3: Apply log property

Using the property \(\log_{a}a^{x}=x\), here \(a = 10\) and \(x=-1\), so \(\log_{10}10^{-1}=-1\).

Answer:

\(-1\)