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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 29
Chapter 5, Problem 29

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. grapefruit, 6.3×\(\times\)10-4

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 for grapefruit: \([H_3O^+] = 6.3 \times 10^{-4}\).
Substitute the given concentration into the pH formula: \(\text{pH} = -\log_{10}(6.3 \times 10^{-4})\).
Use the logarithm property for products: \(\log_{10}(a \times b) = \log_{10}(a) + \log_{10}(b)\), so rewrite as \(\text{pH} = - (\log_{10}(6.3) + \log_{10}(10^{-4}))\).
Calculate the logarithms separately and combine them, then round the final pH value 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.

Logarithms and Their Properties

Logarithms are the inverse operations of exponentiation. Understanding how to calculate and manipulate logarithms, especially base-10 logs, is essential for converting hydronium ion concentrations into pH values. For example, log(10^-4) = -4.
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Scientific Notation

Scientific notation expresses very large or small numbers as a product of a number between 1 and 10 and a power of 10. It simplifies calculations and helps interpret values like 6.3 × 10^-4, which represents the hydronium ion concentration in this problem.
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