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 ?

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.