Evaluate or simplify the expression without using a calculator.
-Use the formula $R = \log \left( \frac { a } { T } \right) + B$ to find the intensity $R$ on the Richter scale, given that amplitude a is 431 micrometers, time T between waves is $2.4$ seconds, and B is $2.4$. Round answer to one decimal place.
A) $4.7$
B) $7.6$
C) $2.3$
D) $9.3$

Question

Quizplus · Accepted Answer

To find the intensity $R$ on the Richter scale, substitute the given values into the formula: $R = \log \left( \frac { 431 } { 2.4 } \right) + 2.4$. Simplifying inside the logarithm gives $\log \left( 179.5833\right) + 2.4$. Without calculating the exact value of the logarithm, we know that $\log(100) = 2$ and $\log(1000) = 3$, so $\log(179.5833)$ will be between 2 and 3. Adding 2.4 to a value between 2 and 3 will give a result close to 4.7 when rounded to one decimal place.

Evaluate or Simplify the Expression Without Using a Calculator R=log⁡(aT)+BR = \log \left( \frac { a } { T } \right) + BR=log(Ta​)+B

Evaluate or Simplify the Expression Without Using a Calculator $R = \log \left( \frac { a } { T } \right) + B$