`27^(4x-1)=9^(3x+8)`

To solve, factor the 9 and 27.

`(3^3)^(4x-1)=(3^2)^(3x+8)`

To simplify each side, apply the exponent rule `(a^m)^n=a^(m*n)` .

`3^(3*(4x-1))=3^(2*(3x+8))`

`3^(12x-3)=3^(6x+16)`

Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right.

`12x-3=6x+16`

`12x-6x=3+16`

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`27^(4x-1)=9^(3x+8)`

To solve, factor the 9 and 27.

`(3^3)^(4x-1)=(3^2)^(3x+8)`

To simplify each side, apply the exponent rule `(a^m)^n=a^(m*n)` .

`3^(3*(4x-1))=3^(2*(3x+8))`

`3^(12x-3)=3^(6x+16)`

Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right.

`12x-3=6x+16`

`12x-6x=3+16`

`6x=19`

`x=19/6`

**Therefore, the solution is `x = 19/6` .**