Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.5 - Common and Natural Logarithms - 9.5 Exercises - Page 621: 42

Answer

$\text{pH }5.9$

Work Step by Step

Using $ pH=-\log[H_3O^+] $ or the formula for the pH of a solution, with $H_3O^+= 1.3\times10^{-6} $, then \begin{align*}\require{cancel} pH&=-\log(1.3\times10^{-6}) \\&= -\left(\log1.3+\log10^{-6}\right) &(\text{use }\log_b (xy)=\log_b x+\log_b y) \\&= -(\log1.3-6\log10) &(\text{use }\log_b x^y=y\log_b x) \\&= -\left(\log1.3-6(1)\right) &(\text{use }\log10=\log_{10}10=1) \\&= -\log1.3+6 .\end{align*} Using a calculator, the value of $ \log1.3 $ is approximately $ 0.1139 $. Hence, the equation above is equivalent to \begin{align*} pH&\approx-0.1139+6 \\&\approx 5.9 .\end{align*} Hence, Tuna has $ \text{pH }5.9 $.
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