Word Problem:

On September 26 2001, an earthquake in North Bay measured 5.0 on the Ritcher scale. What is the magnitude of an earthquake 3 times as intense as North Bay's earthquake?

My Work So Far:

Let $\displaystyle I_B$ represent the earthquake in North Bay

Let $\displaystyle I_F$ represent the earthquake in ________?

North Bay:

$\displaystyle 5 = log(\frac {I_B}{I_o})$

$\displaystyle (\frac {I_B}{I_o}) = 10^{5}$

$\displaystyle I_B = 10^{5} I_o$

Somewhere Else:

$\displaystyle 3r = log(\frac {I_F}{I_o})$

$\displaystyle (\frac {I_F}{I_o}) = 10^{3r}$

$\displaystyle I_F = 10^{3r} I_o$

Comparison:

$\displaystyle \frac {I_B}{I_F} = \frac {10^{5} I_o}{10^{3r} I_o}$

$\displaystyle \frac {I_B}{I_F} = \frac {10^{5}}{10^{3r}}$

$\displaystyle {I_B}= 10^{5-3r}I_o$

Am I doing this right? If I am, what should I do next? If I'm not, where did I make my mistake and how should I correct it?

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Answer: 5.477