Prove the formula log a b log b a = 1 for all positive numbers a, b

Question:

Prove the formula log_a b log_b a = 1 for all positive numbers a, b with a ≠ 1 and b ≠ 1.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 01, 2023 02:49 AM

See More Questions

Two springs are attached to an object of mass, 11 kg on a horizontal frictionless surface. Springs constant of both springs is 650N/m. Object is pulled away from the point A, a distance x=8cm as seen...
By using a substitution, prove that for all positive numbers x and y, xy X 7dt = 7 dt.
Find: Median of the data. Classes Frequency Cumulative.
Suppose that in a particular area the consumption of water varies tremendously throughout the year, with average household summer use exceeding winter use by a great deal. What effect would this have...
AFW Industries has 200 million shares outstanding and expects earnings at the end of this year of $700 million. AFW plans to pay out 60% of its earnings in total, paying 40% as a dividend and using...
How many ways are there to choose a dozen donuts from 20 varieties a) If there are no two donuts of the same variety? b) If all donuts are of the same variety? c) If there are no restrictions? d) If...
The minimum wage. The federal government sets the minimum hourly wage that employers can pay a worker. Labor wants a high minimum wage, but many economists argue that too high a minimum makes...
Salvador Corporation made an investment in Letter.com, Inc., in exchange for 100,000 options to purchase Letter.coms stock at $20 per share. Since the stock options are not marketable, Salvadors...
Scheduled payments of $893 due one year ago and $828 due in four years are to be replaced by two equal payments. The first replacement payment is due in three years and the second payment is due in...
Let Prove that F(x) and cosh 1 x differ by a constant by showing that they have the same derivative. Then prove they are equal by evaluating both at x = 1. 25 F(x)=xx-1-2 2 - 1 dt
Develop an elegant approach to the exponential and logarithm functions. Define a function G for x > 0: This exercise proceeds as if we didnt know that G(x) = ln x and shows directly that G has all...
a. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years, b. If a person is randomly selected,...
Write down at leastfive items (durable goods, not food) that you purchase and their sourcing (where each is from). For example, a shirt may be assembled in China, designed in the US, and made from...
I agree that overtime can be tricky in different countries. As we've seen with piecework, it is hard to implement it in countries where people are not motivated to work past their regular hours, even...
time (in seconds). Find a formula for 1, if V = 5t(t Suppose that an object's acceleration function is given by a = 4t+ 6. The object's initial velocity is 4, and the initi position is 9. Find the...
Determine the specific major and foundational managerial discoveries and findings from each era as most pivotal for management evolution (Early Management Era, Social Management Era, Scientific...
Identify the three major pricing strategies and discuss the important key factors that impact setting prices. Explain what time of pricing strategy your assigned brand uses and why you believe this...
As a certified public accountant, you have been contacted by Joe Davison, CEO of Sports-Pro Athletics, Inc., a manufacturer of a variety of athletic equipment. He has asked you how to account for the...
According during to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,088 in 2018. Consider the population of "last-minute" filers who mail...
According to Borjas (2003), immigration to the United States increased the labor supply of working men by 11.0% from 1980 to 2000, and reduced the wage of the average native worker by 3.2%. From...
Keeler et al. (2004) estimate that the U.S. Tobacco Settlement between major tobacco companies and 46 states caused the price of cigarettes to jump by 45 per pack (21%) and overall per capita...
In a commentary piece on the rising cost of health insurance ("Healthy, Wealthy, and Wise," Wall Street Journal, May 4, 2004, A20), economists John Cogan, Glenn Hubbard, and Daniel Kessler stated,...
C0 = 10.648148 b) ( 4 Marks ) As of now, Given the above conditions on the option, what is the intrinsic value of the call option? What is the time value of the call option?
interest revenue 19,500 retained earning,end 5,000 selling expenses 145,00 prepaid insurance 20,000 loss and disposal of a business (discountied),net 28,000 income from operation 140,000 unearned...
cost that do not extend the acid capacity or it's useful life, but merely maintained the assd, or restore it to working order are recorded as losses True or False

Prove the formula log a b log b a = 1 for all positive numbers a, b

Question:

Step by Step Answer:

loga b In b In a ...View the full answer

Calculus

Students also viewed these Mathematics questions