Math

posted by .

Please show your solution and how you did it. Thank you so much.

1.If x and y are positive numbers such that x^y=y^x and y =2012x, what is x?

2. What powers of two prime numbers will give a product of 1000...000(this sign --> { below the 1000...000 and below this { telling 2012 zeros )

  • Math -

    Please provide the solution, how you did it pleaseeee<3 Thank youuuuuuuuuu

  • Math -

    1.
    x^y = y^x ,and y = 2012x

    x^(2012x) = (2012x)^x
    take ln of both sides, and use log rules

    2012x lnx = x ln(2012x)
    2012x lnx = x (ln2012 + lnx)
    2012 lnx = ln 2012 + lnx
    2012 lnx - lnx = ln2012
    lnx(2012 - 1) = ln2012
    lnx = ln2012 /2011 = .003782637
    x = e^.00378... = 1.003789801
    y = 2012(1.0037...) = 2019.625079

    YOu can check with your calculator, the values work in the original equation x^y = y^x

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    You can use the prime factorization of a number, written as the product of powers of prime numbers, to find the number of factors the number has. First, express the number as a product of powers of prime numbers; for example, 36=2 …
  2. math

    You can use the prime factorization of a number, written as the product of powers of prime numbers, to find the number of factors the number has. First, express the number as a product of powers of prime numbers; for example, 36=2 …
  3. math

    The Florida Lottery is made up of the numbers 1-49. My mother has observed that the winning numbers many times are prime numbers. 1.List the prime numbers from 1-49: 2.What is the probability of a prime number being picked randomly …
  4. math

    The Florida Lottery is made up of the numbers 1-49. My mother has observed that the winning numbers many times are prime numbers. 1.List the prime numbers from 1-49: 2.What is the probability of a prime number being picked randomly …
  5. math

    which of these statements about prime and composite numbers is true?
  6. math

    How do the ideas of divisibility and multiples relate to the study of fractions?
  7. Math

    What powers of two prime numbers will give a product of 1000...000(this sign --> { below the 1000...000 and below this { telling 2012 zeros ) Please show your solution and how you did it. Thank you so much.
  8. MATHS!!!Please HELP..:'(

    What is the sum of all integer values of n satisfying 1≤n≤100, such that (n^2)−1 is a product of exactly two distinct prime numbers?
  9. Math (Complex Numbers)

    Let N be the sum of all prime powers that can be written as 4^n+n^4 for some positive integer n. What are the last 3 digits of N?
  10. math

    Circle the prime numbers in the following set of numbers. Show your work. 953, 1,427, 2,971 I can tell whether each number is prime but I am having a hard time with individual numbers

More Similar Questions