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 ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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