`3^(3x-7)=81^(12-3x)` Solve the equation.

Expert Answers

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`3^(3x-7)=81^(12-3x)`

To solve, factor 81.

`3^(3x-7)=(3^4)^(12-3x)`

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

`3^(3x-7)=3^(4*(12-3x))`

`3^(3x-7)= 3^(48-12x)`

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.

`3x-7=48-12x`

`3x+12x=48+7`

`15x=55`

`x=55/15`

`x=11/3`

Therefore, the solution is `x=11/3` .

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