Determine the probability that the element from the set {1,2,3,4,5,6,7,8} to be solution of the equation 3^(2x-6)=81 ?

Let's recall the formula of
probability:

P = m / n, where m is the number of ways an
event, that has the property "solution of the equation: 3^(2x-6)=81" can occure and n is
the total number of possible outcomes.

To determine the
value for m, we have to solve, at first, the
equation

3^(2x-6)=81

We've
noticed that 81 is a power of 3 and we'll create matching bases, writting 81 =
3^4

3^(2x-6)=3^4

Since the
bases are matching, we'll apply one to one
property:

2x-6=4

We'll add 6
both
sides:

2x=6+4

x=10/2

x=5

Knowing
that x=5 is the single root for the equation 3^(2x-6)=81, that means that
m=1.

P=m/n, where m=1 and n=8 (8 countable elements in the
set)

The probability of an element from the
given set to be the solution of the equation 3^(2x-6)=81
is: P=1/8.