15^(2x-3)=3^x*5^(3x-6) x=?

We notice that we can write 15 =
3*5

We'll raise to 2x-3 both
sides:

15^(2x-3) =
3^(2x-3)*5^(2x-3)

We'll re-write the
equation:

3^(2x-3)*5^(2x-3) =
3^x*5^(3x-6)

We'll divide by 3^x and we'll
get:

3^(2x-3)*5^(2x-3)/3^x =
5^(3x-6)

We'll divide by
5^(2x-3):

3^(2x-3)/3^x =
5^(3x-6)/5^(2x-3)

We'll subtract the
exponents:

3^(2x - 3 - x) = 5^(3x - 6 - 2x +
3)

We'll combine like terms inside
brackets:

3^(x - 3) = 5^(x -
3)

We'll re-write the
equation:

3^x*3^-3 =
5^x*5^-3

3^x/3^3 =
5^x/5^3

We'll create matching bases. We'll divide by
5^x:

3^x/5^x*3^3 = 1/5^3

We'll
multiply by 3^3:

3^x/5^x =
3^3/5^3

(3/5)^x =
(3/5)^3

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

x =
3

The solution of the equation is x =
3.