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 .
Tuesday, June 12, 2012
3^(3x-7)=81^(12-3x) Solve the equation.
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