How is earthquake intensity measured using the Richter scale?

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    Calculus
In summary, the conversation discusses how to convert logarithmic equations into exponential form and vice versa, as well as how to solve for x in these equations. It also explores the Richter scale used to measure earthquake intensity and its relation to logarithmic equations. The key concepts are understanding the properties of logarithms and exponents and being able to apply them in various scenarios. The conversation also emphasizes the importance of practice and studying to improve mathematics skills.
  • #1
vadlamudit
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how do you express in exponential form?
a) log (4) 16 = 2 ans: 16 = 4^2
b) log (16) 2 = 1/4 ans: 2 = 16^1/4
c) log (2) 1/16 = -4 ans: 1/16 = 2^-4
d) 2^5 = 32 how do you express in log form? ans: 5 = log (2) 32
e) 36^1/2 = 6 ans: 1/2 = log (36) 6
f) 4^-4 = 1/81 ans: -4 = log (3) [1/81]
g) log (3) 81 =? ans: 4
h) log (2) 1/64 ? ans: -6
i) log (3) (27)^1/2 ans: 3/2
j) log (1/2) 4 ans: -2
k) log(10) 5 - log (10) 50 ans: -1
l) log (6) 18 + log (6) 12 ans: 3

how do you conve\rt to exponential form and solve for x?
a) log (2) 5x = 7 ans: 128/5
b) log (10) x^3 = 18 ans: 10^6
c) 2log (4) [8x] = 5 ans: 4
d) log(5) [3x^2] - log(5) [15x] = 3 ans: 625
e) log (x) 64 = 3/2 ans: 16

Which is larger?
a) 2log5 or 3log3 ans: 3 log 3
b) 1/2 log(2) 16 or 1/3 log (3) 27? ans: 1/2 log (2) 16

HOw do you solve for x:
a) 10^5x = 25 ans: 1/5 log 25 = 0.279
b) 2^x = 1000 ans: 3/log 2 = 9.965
c) 4^2x = 200 ans: log 200/log 16 = 1.9109

9) magnitudes of earthquatkes are measured by using the richeter scale. on thisscale, the

magnitude R of an earthquake is given by R = log (10)[I/I (subscript 0)]

wher I is the intensity of the earthquake being measured and I 0 is a fixed standanrd

intensity used for comparison.
a) show that if an earthquake measures R = 4 on the richter scale, then its intensity is 10

000 times teh standard.


b) how many times morei intense is an earthquake measuring R = 6 than one measruing R = 4?
ans: 100 times more intense
c) the mexico city eartquake of 1985 measured 8.1 on the richeter scale. express its

intensity in terms of the standard intensity.
ans:1.26 x 10^8 Io
 
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  • #2
We are happy to help you with your homework, but we don't want to do it for you. Besides, these problems aren't that difficult.

Have you tried them? Can you show us how you started?

Do that, and we will help through the rough spots.
 
  • #3
yes
this is a very easy question
i suggest you read the book
it more helpful to impreove your mathematics skill
 

What is calculus and why is it important?

Calculus is a branch of mathematics that deals with the study of continuous change and motion. It is used to understand and describe various phenomena in the physical world, such as the motion of objects, the growth of populations, and the rate of change in natural phenomena. It is an essential tool in many fields of science, including physics, engineering, and economics.

What are some common applications of calculus?

Calculus has numerous real-world applications, including predicting the trajectory of projectiles, designing buildings and bridges, optimizing business strategies, and understanding the behavior of biological systems. It is also used in the creation of computer graphics, weather forecasting, and medical imaging.

What is the difference between differential and integral calculus?

Differential calculus is concerned with finding the instantaneous rate of change of a function, while integral calculus deals with calculating the total accumulation of a quantity over a given interval. In simpler terms, differential calculus focuses on the slope of a curve, while integral calculus focuses on the area under the curve.

What are some common challenges in solving calculus problems?

One of the most common challenges in solving calculus problems is understanding the underlying concepts and principles. It is also important to have a strong foundation in algebra, trigonometry, and geometry. Another challenge is being able to visualize and interpret mathematical concepts in real-world situations.

How can I improve my understanding and skills in calculus?

To improve your understanding and skills in calculus, it is important to practice regularly and work through various problems. You can also seek help from teachers, tutors, or online resources. It is also helpful to try to apply calculus concepts to real-world scenarios to better understand their practical applications.

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