The wave amplitude A of the earthquake was 66.81 times [tex]A_{o}[/tex].
We have Richter scale measurement of 4.2.
We have to find approximately how many times stronger the wave amplitude A of the earthquake was than [tex]A_{o}[/tex]
Simplify the following function -
f(x) = [tex]e^{log x}[/tex] and express it in single power of x.
Let [tex]e^{log x}[/tex] = z
Taking natural log both sides -
log ([tex]e^{log x}[/tex]) = log (z)
log (x) log (e) = log (z)
log (x) = log (z) { log (e) = 1 }
z = [tex]e^{log x}[/tex] = x
In the question, it is given that -
R = 4.2 and [tex]R = log(\frac{A}{A_{o} } )[/tex]
Therefore -
4.2 = log ([tex]\frac{A}{A_{o} }[/tex])
Taking exponential on both sides -
[tex]e^{(4.2)}=e^{log^{\frac{A}{A_{o} } } }[/tex]
66.81 = [tex]\frac{A}{A_{o} }[/tex]
A = 66.81 [tex]A_{o}[/tex]
Hence, the wave amplitude A of the earthquake was 66.81 times [tex]A_{o}[/tex].
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