csat-suneung 2008 Q22

csat-suneung · South-Korea · csat__math-humanities 4 marks Laws of Logarithms Logarithmic Formula Application (Modeling)
The average number of earthquakes $N$ with magnitude $M$ or greater occurring in a region over one year satisfies the following equation.
$$\log N = a - 0.9 M ( \text{ where } a \text{ is a positive constant } )$$
In this region, earthquakes with magnitude 4 or greater occur on average 64 times per year. Earthquakes with magnitude $x$ or greater occur on average once per year. Find the value of $9 x$. (Use $\log 2 = 0.3$ for the calculation.) [4 points]
The average number of earthquakes $N$ with magnitude $M$ or greater occurring in a region over one year satisfies the following equation.

$$\log N = a - 0.9 M ( \text{ where } a \text{ is a positive constant } )$$

In this region, earthquakes with magnitude 4 or greater occur on average 64 times per year. Earthquakes with magnitude $x$ or greater occur on average once per year.\\
Find the value of $9 x$. (Use $\log 2 = 0.3$ for the calculation.) [4 points]