Prove that log b (n) =1/log n (b) for any positive integers b > 1 and n

Question:

Prove that log_b (n) =1/log_n (b) for any positive integers b > 1 and n > 1.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Precalculus

ISBN: 9781938168345

1st Edition

Authors: Jay Abramson

See More Books

Question Posted: Jun 02, 2022 03:16 AM

See More Questions

Prove or disprove: If m, n are positive integers and m, n are perfect squares, then m + n is a perfect square.
Prove that if n and k are integers with 1 ¤ k ¤ n, then a) Using a combinatorial proof. b) Using an algebraic proof based on the formula for (nr) given in Theorem 2 in Section 6.3. k...
Prove or disprove that if m and n are integers such that mn = 1, then either m = 1 and n = 1, or else m = 1 and n = 1.
Troy Engines, Ltd., manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the carburetors. An...
How can you effectively communicate with someone who has difficulty with the English language?
For each of the following items, indicate whether it would appear on the cash flow statement as cash from operations, an investing cash flow, or a financing cash flow, or that it wouldn't have an...
Suppose that the recycle times of two cameras are recorded. The extension of the positive real line $R$ is to take the sample space to be the positive quadrant of the plane \[ S=R^{+} \times R^{+}...
If you were trying to assess the financial health of a government administered pension plan, which financial statements or schedules would you review and why?
Write a Python program to compute the following two problems and share a link to your work in the box below. 1. lim x 0 sin(x) X d 2. (sin(a)) dx
Vebco Water and Gas received a contract for a seawater desalination plant wherein the company expected to make a 28% rate of return on its investment. (a) If Vebco invested $8 million the first year,...
For the following exercises, use the one-to-one property of logarithms to solve. ln(x 2) ln(x) = ln(54)
For the following exercises, refer to Table 10. Use a graphing calculator to create a scatter diagram of the data. 1 f(x) 7.5 8 2 6 3 5.2 4 4.3 Table 10 5 3.9 6 3.4 7 3.1 8 2.9
The paper Predictors of Complementary Therapy Use Among Asthma Patients: Results of a Primary Care Survey (Health and Social Care in the Community [2008]: 155 164) described a study in which each...
Lulu Enterprises began the year with total liabilities of $188,000 and total stockholders equity of $330,000. Using this information, answer each of the following independent questions. a) If Lulu's...
Type or paste question here 1. EX.12.01.ALGO eBook Show Me How Average Rate of Return The following data are accumulated by Watershed Inc. in evaluating two competing capital investment proposals:...
Answer the following simple interest questions: 1. Jeff borrowed $25 from his dad to buy a fishing license and promised to pay his dad back in one month. His dad agreed, but said that Jeff must pay...
B Assume company A owns 40% of Company and has the investment recorded on their balance sheet using the Equity Method. Company B has $160 of income in a year. How much affiliate income should company...
write a literature review on the synthesis of flexible latent heat storage material and examination of its thermal performances?
Consider the following three mutually exclusive alternatives: For what range of values of MARR is Alt. C the preferred alternative? Put your answer in the following form: "Alternative C is preferred...
Write an essay describing the differing approaches of nursing leaders and managers to issues in practice. To complete this assignment, do the following: 1. Select an issue from the following list:...
When graphing an inequality in two variables, if the inequality is strict use ________; if the inequality is nonstrict use a________mark.
The graph of the corresponding equation of a linear inequality is a line that separates the xy-plane into two regions. The two regions are called_______.
True or False. The graph of a system of inequalities must have an overlapping region.
Does the concept of revenue less expense equaling an increase in equity or fund balance make sense to you? If not, why not?
Explain the arbitrage strategies employed by Long Term Capital Management (LTCM) and why such strategies may be considered well-founded and explain how basis risk contributed to LTCM's ultimate...
How might free cash flow impact financing and investing decisions for a company like Bath & Body Works?

Prove that log b (n) =1/log n (b) for any positive integers b > 1 and n

Question:

Step by Step Answer:

log b n 1log n b we ...View the full answer

Precalculus

Students also viewed these Mathematics questions