Question

For what value of x does 64^3x = 512^2x+12

Answer 1

no solution

Explanation:

`Use:\\\\(a^n)^m=a^(nm)\\--------------\\64=2^6\\512=2^9\\\\\text{therefore}\\\\64^(3x)=512^(2x+12)\\\\(2^6)^(3x)=(2^9)^(2x+12)\\\\2^((6)(3x))=2^((9)(2x+12))\iff6(3x)=9(2x+12)\\\\18x=9(2x+12)\qquad\text{divide both sides by 9}\\\\(18x)/(9)=(9(2x+12))/(9)\\\\2x=2x+12\qquad\text{subtract 2x from both sides}\\2x-2x=2x-2x+12\\\\0=12\qquad\bold{FALSE}`