csat-suneung 2008 Q22

csat-suneung · South-Korea · csat__math-science 4 marks Exponential Equations & Modelling Solve Exponential Equation for Unknown Variable
In a certain region, the average number of earthquakes $N$ with magnitude $M$ or greater occurring in 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]
In a certain region, the average number of earthquakes $N$ with magnitude $M$ or greater occurring in 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]