We have to solve for x given the equation: 3^(4x-3)*5^(7x-4)=3^3x*5^(8x-7)

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

=> 3^4x*3^-3*5^7x*5^-4 = 3^3x*5^8x*5^-7

=> (3^4x/3^3x)*(3^-3)*(5^7x/5^8x)*(5^-4/5^-7) = 1

=> (3^x)*(3^-3)*(1/5^x)*(5^3) = 1

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

As the base is equal we equate the exponent.

=> x= 3

**The required value of x is x = 3.**