Question

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

Answer 1

Answer:

$\large\boxed{x=\dfrac{17}{10}=1.7}$

Step-by-step explanation:

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