Before the invention of calculators, logarithms took much longer to evaluate. (Think of the older generations who went to college in the 1920s... The math they learned was the same, but was all done BY HAND). In the back of their textbooks, they had appendices that looked like this: Prime In(Prime) log(Prime) In(2) = 0.6931 log(2) = 0.3010 In(3) = 1.0986 log(3) = 0.4771 In(5) = 1.6094 log(5) = 0.6990 %3D 5. In(7) = 1.9460 log(7) = 0.8451 In(11) = 2.3979 | log(11) = 1.0414 %3D 11 %3D Using the fact that the number 679, 140 = 2 * 32 *5 * 7 *11 as its prime factorization: (a) use the properties of logs to expand In(679, 140) as far as possible Hint... expand In(22 * 32 *5 * 7° * 11) as far as possible (b) using the table above, plug in the values for each logarithm to four decimal places. What is your answer using the rounded values in the table? (c) Using your calculator, what is the value of In(679140) to 6 decimal places? Explain your answer and why it is similar/different than the answer in part (b) 3.

Before the invention of calculators, logarithms took much longer to evaluate. (Think of the older generations who went to college in the 1920s... The math they learned was the same, but was all done BY HAND). In the back of their textbooks, they had appendices that looked like this: Prime In(Prime) log(Prime) In(2) = 0.6931 log(2) = 0.3010 In(3) = 1.0986 log(3) = 0.4771 In(5) = 1.6094 log(5) = 0.6990 %3D 5. In(7) = 1.9460 log(7) = 0.8451 In(11) = 2.3979 | log(11) = 1.0414 %3D 11 %3D Using the fact that the number 679, 140 = 2 * 32 5 7 11 as its prime factorization: (a) use the properties of logs to expand In(679, 140) as far as possible Hint... expand In(22 32 5 7° * 11) as far as possible (b) using the table above, plug in the values for each logarithm to four decimal places. What is your answer using the rounded values in the table? (c) Using your calculator, what is the value of In(679140) to 6 decimal places? Explain your answer and why it is similar/different than the answer in part (b) 3.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: why is e and the natural logarithm, rather than other bases, are used in so many situations

A: We have to explain why is natural logarithm is used more.

Q: Find a number E such that log (5z + 1) = 2

A: The solution is given below.

Q: Evaluate each of the following, to at least 3 decimal places. a. log (10,000,000) 1 1000 b. log c.…

A: The given logarithm values, a) log10,000,000 b) log11000 c) log70. We have to find the solution for…

Q: The question is in the pic attached. I’m having trouble converting into exponential form. Thank you.…

A: Converting logarithmic equations in to exponential form.If the base of the logarithm is 10, then the…

Q: If log A = 4.04 and log B = 1.53, what is the value of log hundredth? Answer: to the nearest

Q: Solve each of the following for x. (Hint: Use the properties discussed in class or your…

Q: (9) The Richter scale for the intensity of earthquakes is given by the formula W R= log Wo |3| Where…

Q: To four decimal places, the values of log 102 and log 1025 are shown below. Evaluate the logarithm,…

Q: What kind of number is the number e? It's an irrational number, meaning it cannot be written as a…

A: Rational number: the numbers which can be written in the form of fraction they are known as rational…

Q: Complete the following table of logarithms without using a calculator; then, answer the questions…

Q: Use the change of base formula to compute log, 5. Round your answer to the nearest thousandth.

A: The given logarthim log8 5.

Q: Evaluate each of the following, to at least 3 decimal places. a. log (1,000,000) = b. 1 log 100 c.…

A: To find the given values:a) b) c) Logarithm Formula:

Q: (QUES-7337) Recall the compound interest formula A= a(1 + ". Use the definition of a logarithm along…

Q: Simplify log(60)+log(15)−log(2)−log(2) as a single logarithm

Q: If log 27 = 1.431, then find out the value of log 9

A: Given,

Q: When working with extremely large numbers, it is sometimes necessary to interconvert between natural…

A: we need to find log10(x) where ln(x)=43.098

Q: given that log109=0.95 and log102= 0.30 to two decimals places evaluate the following log10900

Q: (C) If a student asked why you can't take the logarithm of a negative number and get a real number,…

A: Logarithmic function:- In mathematics, the opposite of exponentiation is the logarithm. This shows…

Q: Most calculators can find logarithms with base 10and base e. To find logarithms with different…

A: logba = (logca)/(logcb), where a,b,c > 0 and b ≠ 1, c ≠ 1.

Q: Given that log5(2)= 2.32 and log5(3)= 1.46 What is log5(4/3)?

Q: Suppose that logb 3 = 0.2 and that logb 13 = 0.5. Use the properties of logarithms to find: logb 39…

Q: QUESTION 1 Which of the following is equivalent to 2log3(b)+5log3(x)– log3(a)? log3 a B. log3(b²+x$…

A: Here we are given an expression 2log3(b)+5log3(x)-log3(a) We have to found its equivalent form by…

Q: Assume you need to calculate log b N , but your calculator has only a log w button. Derive…

A: We have to derive the formula for logbN in terms of logw.

Question

Before the invention of calculators, logarithms took much longer to evaluate. (Think of the
older generations who went to college in the 1920s... The math they learned was the same,
but was all done BY HAND). In the back of their textbooks, they had appendices that looked
like this:
Prime
In(Prime)
log(Prime)
In(2) = 0.6931
log(2) = 0.3010
In(3) = 1.0986
log(3) = 0.4771
In(5) = 1.6094
log(5) = 0.6990
%3D
5.
In(7) = 1.9460
log(7) = 0.8451
In(11) = 2.3979 | log(11) = 1.0414
%3D
11
%3D
Using the fact that the number 679, 140 = 2 * 32 *5 * 7 *11 as its prime factorization:
(a) use the properties of logs to expand In(679, 140) as far as possible Hint... expand
In(22 * 32
*5 * 7° * 11) as far as possible
(b) using the table above, plug in the values for each logarithm to four decimal places. What
is your answer using the rounded values in the table?
(c) Using your calculator, what is the value of In(679140) to 6 decimal places? Explain your
answer and why it is similar/different than the answer in part (b)
3.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

given data

part (a)

part (b)

part (c)

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The question is from Numberr Theory..
If Log10(5x) = 2, then x = a. 1 b. 4 c. 20 d. 25
Determine the logarithms of the following numbers: log 100,000 = log (1 X 107) = log (1.0 X 10-3) = – log (1 X 10-9) = if you need to count this as multiple questions you can
Be simple when explain and anwer the hole question