The wave amplitude A of the earthquake was 66.81 times \(A_{o}\).
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 \(A_{o}\)
Simplify the following function -
f(x) = \(e^{log x}\) and express it in single power of x.
Let \(e^{log x}\) = z
Taking natural log both sides -
log (\(e^{log x}\)) = log (z)
log (x) log (e) = log (z)
log (x) = log (z) { log (e) = 1 }
z = \(e^{log x}\) = x
In the question, it is given that -
R = 4.2 and \(R = log(\frac{A}{A_{o} } )\)
Therefore -
4.2 = log (\(\frac{A}{A_{o} }\))
Taking exponential on both sides -
\(e^{(4.2)}=e^{log^{\frac{A}{A_{o} } } }\)
66.81 = \(\frac{A}{A_{o} }\)
A = 66.81 \(A_{o}\)
Hence, the wave amplitude A of the earthquake was 66.81 times \(A_{o}\).
To solve more questions on logarithms, visit the link below -
https://brainly.com/question/14406258
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