Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.4 Evaluation Logarithms and the Change-of-Base Theorem - 4.4 Exercises - Page 457: 37

$4.6$; poor fen

We are given that $pH$ between $6.0$ and $7.5$ is rich fen and between $6.0$ and $3.0$ is poor fen or less is bog. Apply logarithmic property : $\log m+ \log n=\log (mn)$ The given expression can be written as: $pH=-[\log 2.49 + \log 10^{-5}]$ Now, apply logarithmic property : $\log a^ b=b \log a$ Therefore, we have: $pH=-[\log 2.49 + \log 10^{-5}]=- \log 2.49 - (-5) \log 10$ or, $pH=-\log 2.49 +5 =4.6$ Therefore, our answer is: $4.6$; poor fen