# Question Video: Solving Logarithmic Equations in a Real-World Context Mathematics

The pH of a solution is given by the formula pH = −log (𝑎_(H+)), where 𝑎_(H+) is the concentration of hydrogen ions. Determine the concentration of hydrogen ions in a solution whose pH is 8.4.

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### Video Transcript

The pH of a solution is given by the formula pH is equal to negative log of 𝑎 sub H+, where 𝑎 sub H+ is the concentration of hydrogen ions. Determine the concentration of hydrogen ions in a solution whose pH is 8.4.

When the pH is equal to 8.4, 8.4 is equal to negative log of 𝑎 sub H+. We are trying to work out this value which is the concentration of hydrogen ions. We recall that when a logarithm is written without a base, it is assumed to be base 10. Log 𝑥 is the same as log base 10 of 𝑥. We can multiply both sides of our equation by negative one such that negative 8.4 is equal to log base 10 of 𝑎 sub H+. We know that a logarithmic function is the inverse of an exponential function. If 𝑥 is equal to log base 𝑎 of 𝑦, then 𝑎 to the power of 𝑥 is equal to 𝑦. This means that 10 to the power of negative 8.4 is equal to 𝑎 sub H+. The concentration of hydrogen ions is therefore equal to 10 to the power of negative 8.4.

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