Homework Help: Math

Posted by Aliza on Tuesday, December 4, 2012 at 6:51am.

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 - Aliza, Tuesday, December 4, 2012 at 6:52am
Please provide the solution, how you did it pleaseeee<3 Thank youuuuuuuuuu
Math - Reiny, Tuesday, December 4, 2012 at 7:36am
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

Answer this Question

Related Questions

biology - if a solution has a pH of 4 mix to a solution that has a pH of 9 what ...
Math - The following equation has a positive and a negative solution. z-1/z+1 = ...
math - Hello, can someone please enlighten me? MSI means 1000 sq inches, right? ...
MATH,HELP - Can someone show me how to even do this problem. Find all positive ...
MATH - Find the only positive integer whose cube is the sum of the cubes of ...
Algebra II - In an induction proof of the statement 4+7+10+...+(3n-1)=n(3n+5)/2 ...
Algebra 2 - How much pure acid must be added to 6 milliliters of a 5% acid ...
physics - (6.0 Gm)/(3.0 ksec) = ?m/sec Please help me and please show all steps ...
CHEMISTRY..please help..thanks - Calculate the new molarity if each of the ...
math - 2. Simplify. Please be sure to show all of your work. -3(-9) – |-5...

For Further Reading

First Name:
School Subject:
Answer: