What is the solution for x: 3^(x^2-7x+10) - 9^3 = 0

We'll move the number 9^3 to the right
side:

3^(x^2-7x+10) =
9^3

We'll create matching bases both sides. Therefore,
we'll re-write 9^3 = (3^2)^3 = 3^(2*3) = 3^6

We'll re-write
the equation as it follows:

3^(x^2-7x+10) =
3^6

Since the bases are matching now, we'll apply one to
one rule and we'll equate the
superscripts:

(x^2-7x+10)=6

We'll
subtract 6 both
sides:

x^2-7x+10-6=0

x^2-7x+4=0

We'll
apply quadratic
formula:

x1=[7+sqrt(49-16)]/2

x1=(7+sqrt33)/2

x2=(7-sqrt33)/2

The
possible values of the exponent x are: {(7-sqrt33)/2
;(7+sqrt33)/2}.