Question

If 5+ 20 -22-3х - 10.2-2x+5, what is the value of х?

Answer 1

3

Explanation:

`5+20\cdot2^(2-3x)=10\cdot2^(-2x)+5\qquad\text{subtract 5 from both sides}\\\\20\cdot2^(2-3x)=10\cdot2^(-2x)\qquad\text{divide both sides by 10}\\\\2\cdot2^(2-3x)=2^(-2x)\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\2^(1+2-3x)=2^(-2x)\\\\2^(3-3x)=2^(-2x)\iff3-3x=-2x\qquad\text{subteact 3 from both sides}\\\\-3x=-2x-3\qquad\tex\qquad\text{add}\ 2x\ \text{to both sides}\\\\-x=-3\qquad\text{change the signs}\\\\x=3`