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Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 4 - Inverse, Exponential, and Logarithmic FunctionsProblem 31
Chapter 5, Problem 31

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. crackers, 3.9×\(\times\)10-9

Verified step by step guidance
1
Recall the formula to find pH from the hydronium ion concentration \([H_3O^+]\): \(\text{pH} = -\log_{10}([H_3O^+])\).
Identify the given hydronium ion concentration: \([H_3O^+] = 3.9 \times 10^{-9}\).
Substitute the given concentration into the pH formula: \(\text{pH} = -\log_{10}(3.9 \times 10^{-9})\).
Use logarithm properties to simplify: \(\log_{10}(a \times b) = \log_{10}(a) + \log_{10}(b)\), so \(\text{pH} = - (\log_{10}(3.9) + \log_{10}(10^{-9}))\).
Calculate the values of the logarithms separately and then combine them to find the pH, rounding the final answer to the nearest tenth.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH and Hydronium Ion Concentration

pH is a measure of the acidity of a solution and is calculated as the negative logarithm (base 10) of the hydronium ion concentration, [H3O+]. The formula is pH = -log[H3O+]. A lower pH indicates higher acidity, while a higher pH indicates lower acidity or basicity.

Logarithms and Their Properties

Logarithms are the inverse operations of exponentiation. Understanding how to calculate and interpret logarithms, especially base 10 logs, is essential for converting hydronium ion concentrations into pH values. Familiarity with log rules helps simplify calculations and interpret results.
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Scientific Notation

Scientific notation expresses very large or very small numbers compactly, such as 3.9 × 10^-9. Recognizing and correctly using scientific notation is important for accurately inputting values into the pH formula and ensuring precise calculations.
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