- Use the basic properties of logarithms to simplify expressions and solve equations
- Combine or separate logarithms using the product and quotient rules
- Use the power rule to simplify logarithms with exponents
- Break down or combine complicated logarithm expressions into simpler forms
- Use the change-of-base formula to calculate and simplify logarithms with different bases
In chemistry, pH is a measure of how acidic or basic a liquid is. It is essentially a measure of the concentration of hydrogen ions in a solution. The scale for measuring pH is standardized across the world, the scientific community having agreed upon its values and methods for acquiring them.
Measurements of pH can help scientists, farmers, doctors, and engineers solve problems and identify sources of problems.
pH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, [latex]a_{H}+[/latex], in a solution.
[latex]\text{pH} =-\log _{10}(a_{{\text{H}}^{+}})=\log _{10}\left({\frac {1}{a_{{\text{H}}^{+}}}}\right)[/latex]
For example, a solution with a hydrogen ion activity of [latex]2.5×{10}^{-6}[/latex] (at that level essentially the number of moles of hydrogen ions per liter of solution) has a pH of [latex]\log_{10}\left(\frac{1}{2.5×{10}^{-6}}\right)=5.6[/latex]
In the next examples, we will solve some problems involving pH.