Question

Solve for x. 8^2x −3 = ( 1 16 )^x − 2 plz help

Answer 1

`\large\boxed{x=(17)/(10)=1.7}`

Explanation:

`8=2^3\\\\(1)/(16)=(1)/(2^4)=2^(-4)\qquad\text{used}\ a^(-n)=(1)/(a^n)\\\\8^(2x-3)=\left((1)/(16)\right)^(x-2)\\\\(2^3)^(2x-3)=(2^(-4))^(x-2)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\2^(3(2x-3))=2^(-4(x-2))\iff3(2x-3)=-4(x-2)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-3)=(-4)(x)+(-4)(-2)\\\\6x-9=-4x+8\qquad\text{add 9 to both sides}\\\\6x=-4x+17\qquad\text{add 4x to both sides}\\\\10x=17\qquad\text{divide both sides by 10}\\\\x=1.7`