SOLUTION: Please help me solve this equation ... Find the value of x satisfying ...{{{2^(3x+1)-3.2^(x)+2^(x+1)=2^x}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help me solve this equation ... Find the value of x satisfying ...{{{2^(3x+1)-3.2^(x)+2^(x+1)=2^x}}}      Log On


   

Question 983632: Please help me solve this equation ... Find the value of x satisfying ...2%5E%283x%2B1%29-3.2%5E%28x%29%2B2%5E%28x%2B1%29=2%5Ex
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!

Let us introduce a new variable.

Let  y  be  2%5Ex:   y = 2%5Ex.

Then you can re-write your equation in the form

2y%5E3 - 3y + 2y = y.

Collect common terms:

2y%5E3 = 2y.

Since  y = 2%5Ex  can not be zero,  you can divide both sides by  2y,  and you will get

y%5E2 = 1.

It implies  y = 1.

Hence,  2%5Ex = 1.

Therefore,  x = 0.

Answer.  x = 0.