Logarithmic Function Context and Data Modeling

What AP Precalc asks here

Logarithmic models compress quantities that range over many orders of magnitude. Standard log scales include pH ($-\log_{10}[\text{H}^+]$), Richter ($\log_{10}(A/A_0)$), and decibels ($10 \log_{10}(P/P_0)$). Reading these scales additively is the most common mistake: a difference of 1 unit corresponds to a multiplicative ratio of 10, not 1. Log models also capture diminishing returns — output grows but ever more slowly.

Take the difference in scale values, then raise 10 to that power for the multiplicative ratio.

Substitute the underlying quantities into the formula and evaluate the log.

Use one data point to find $a$ and another to find $b$ in $y = a + b \log_{10} x$. Then evaluate at a new $x$.