Solve the equation 16 {}^(2x - 3) = 8 {}^(4x) ​

Question

Solve the equation

`16 {}^(2x - 3) = 8 {}^(4x)`
​

Answer 1

n = -3

Explanation:

`16=2^4\\\\8=2^3\\\\16^(2n-3)=8^(4n)\\\\(2^4)^(2n-3)=(2^3)^(4n)\qquad\txt{use}\ (a^n)^m=a^(nm)\\\\2^((4)(2n-3))=2^((3)(4n))\iff4(2n-3)=12n\qquad\text{use the distributive property}\\\\(4)(2n)+(4)(-3)=12n\\\\8n-12=12n\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-12=4n\qquad\text{divide both sides by 4}\\\\(-12)/(4)=(4n)/(4)\\\\-3=n\to n=-3`