What is the probability that the element from the set {1,2,3,4,5,6} to be the root of the equation 4^(2x-5)=64 ?
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
4^(2x - 5) = 64
=> 4^(2x - 5) = 4^3
as 4 is equal we equate the exponent
2x - 5 = 3
=> 2x = 3 + 5
=> x = 8/2
=> x = 4
Now we have the 6 terms of which 4 is one term, so the probability of picking 4 when any number from the set is picked is 1/6.
The required probability is 1/6
Related Questions
- Solve the following simultaneous equations. 2x – 3y = 5 , x – 2y = 4
- 1 Educator Answer
- Find the value of k = ( x^2 - 4 )/ ( 2x -5 ) if the roots of the equation are equal .
- 1 Educator Answer
- Solve the equation square root(x^2-5)-square root(x^2-8)=1
- 1 Educator Answer
Probability formula is presented as a ratio;
P = m / n, where m is the number of ways an event, that has the property "root of the equation: 4^(2x-5)=64 " can occure and n is the total number of possible outcomes.
To find out the value for m, we have to solve, at first, the equation
4^(2x-5)=64
We've noticed that 64 is a multiple of 4 and we'll re-write the equation:
4^(2x-5)=4^3
Since the bases are matching, we'll apply one to one property:
2x-5=3
We'll add 5 both sides:
2x=5+3
x=8/2
x=4
Knowing that x=4 is the single root for the equation 4^(2x-5)=4^3, that means that m=1.
P=m/n, where m=1 and n=6 (6 countable elements in the set)
The probability of an element from the given set to be the solution of the equation 4^(2x-5)=4^3 is: P=1/6.
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers