Questions: Find the indicated value of the logarithmic function. log(1/10)

Solution Steps

To find the value of the logarithmic function \(\log \left(\frac{1}{10}\right)\), we can use the properties of logarithms. Specifically, we can use the property that \(\log \left(\frac{1}{a}\right) = -\log(a)\). Therefore, \(\log \left(\frac{1}{10}\right)\) can be calculated as \(-\log(10)\). Since \(\log(10)\) is 1 (assuming the base is 10), the result will be \(-1\).

To find the value of \( \log \left(\frac{1}{10}\right) \), we can use the property of logarithms that states: \[ \log \left(\frac{1}{a}\right) = -\log(a) \] Thus, we can rewrite our expression as: \[ \log \left(\frac{1}{10}\right) = -\log(10) \]

Since the logarithm base is 10, we know that: \[ \log(10) = 1 \]

Substituting this value back into our expression gives: \[ \log \left(\frac{1}{10}\right) = -1 \]

Final Answer