Magnitute = What?

Question

The Richter scale magnitude, R, of an earthquake of intensity I is defined as R=log (I/I0),where  I0 is a small threshold intensity. Find the magnitude of an earthquake with intensity 55,000,000 I0.

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.
magnitude =

Answer 1

R = log(I/I₀)

 

So, if I = 55,000,000I₀ = (5.5 · 10⁷)I₀, then

 

R = log[(5.5 · 10⁷)I₀/I₀]

 

    = log(5.5 · 10⁷)

 

    = log(5.5) + log(10⁷)

 

    ≈ 0.74 + 7

 

    = 7.74