`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` .
`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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