Question

Solve for X

8^3x-10 =4^6x-27

Thanks in advance!

Answer 1

`8^(3x-10)=4^(6x-27)\\\\(2^3)^(3x-10)=(2^2)^(6x-27)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\2^(3(3x-10))=2^(2(6x-27))\qquad\text{use distributive property}\\\\2^((3)(3x)+(3)(-10))=2^((2)(6x)+(2)(-27))\\\\2^(9x-30)=2^(12x-54)\iff9x-30=12x-54\qquad\text{add 30 to both sides}\\\\9x=12x-24\qquad\text{subtract 12x from both sides}\\\\-3x=-24\qquad\text{divide both sides by (-3)}\\\\\boxed{x=8}`