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
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
We've noticed that 64 is a multiple of 4 and we'll re-write the equation:
Since the bases are matching, we'll apply one to one property:
We'll add 5 both sides:
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.