Given that log x=25 and log 25 approx 1.4, evaluate the given expression without using a calculator.
\[
\log \left(\frac{25}{x}\right)
\]
Answer
Final Answer: The value of the expression \(\log \left(\frac{25}{x}\right)\) is \(\boxed{-23.6}\).
Step 1 ：Given that \(\log x = 25\) and \(\log 25 \approx 1.4\), we need to evaluate the given expression \(\log \left(\frac{25}{x}\right)\) without using a calculator.
Step 2 ：Using the properties of logarithms, the expression \(\log \left(\frac{25}{x}\right)\) can be rewritten as \(\log 25 - \log x\).
Step 3 ：Substitute the given values into the expression, we get \(1.4 - 25\).
Step 4 ：Simplify the expression to get the result as \(-23.6\).
Step 5 ：Final Answer: The value of the expression \(\log \left(\frac{25}{x}\right)\) is \(\boxed{-23.6}\).
