Question

For what value of x does 3^4x=27^x-3? a. –9 b. –3 c. 3 d. 9

Answer 1

`\bf 3^(4x)=27^(x-3)\implies 3^(4x)=(3^3)^(x-3)\stackrel{~\hfill \textit{same base, the exponents must also be the same}}{\implies 3^(4x)=3^(3(x-3))\implies 3^(4x)=3^(3x-9)\qquad } \\\\\\ 4x=3x-9\implies x=-9`