Question

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

Answer 1

Answer:

no solution

Step-by-step explanation:

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