Answer
$8.4$
Work Step by Step
Using $
pH=-\log[H_3O^+]
$ or the formula for the pH of a solution, with $H_3O^+=
3.8\times10^{-9}
$, then
\begin{align*}\require{cancel}
pH&=-\log(3.8\times10^{-9})
\\&=
-\left(\log3.8+\log10^{-9}\right)
&(\text{use }\log_b (xy)=\log_b x+\log_b y)
\\&=
-(\log3.8-9\log10)
&(\text{use }\log_b x^y=y\log_b x)
\\&=
-\left(\log3.8-9(1)\right)
&(\text{use }\log10=\log_{10}10=1)
\\&=
-\log3.8+9
.\end{align*}
Using a calculator, the value of $
\log3.8
$ is approximately $
0.5798
$. Hence, the equation above is equivalent to
\begin{align*}
pH&\approx-0.5798+9
\\&\approx
8.4
.\end{align*}
Hence, the pH of Milk is $
8.4
$.
