Question Expand \( \log \sqrt{x} \) Provide your answer below:

To expand \( \log \sqrt{x} \), we can use the property of logarithms that allows us to bring down the exponent. Since \( \sqrt{x} \) can be rewritten as \( x^{1/2} \), we have: \[ \log \sqrt{x} = \log (x^{1/2}) = \frac{1}{2} \log x. \] Voilà! The expression is expanded neatly! For a bit of historical flair, did you know that logarithms were invented by John Napier in the early 17th century? He aimed to simplify complex calculations, which is why logarithmic tables were so revolutionary for mathematicians and astronomers of his time! If you’re looking to apply this in the real world, consider how logarithms are used in pH calculations in chemistry! The pH scale is a logarithmic scale based on the concentration of hydrogen ions in a solution, making understanding logarithmic functions essential in environmental science and health discussions.