Solve for x: 3^(4x-3)*5^(7x-4)=3^3x*5^(8x-7).

We'll divide both sides by 5^(7x-4) and
3^3x:

3^(4x-3)/3^3x =
5^(8x-7)/5^(7x-4)

We'll subtract the exponents: 3^(4x - 3 -
3x) = 5^(8x - 7 - 7x + 4)

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.