SOLUTION: 2^2x-3 — 2^2x-2 — 1 = 0

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Question 1210236: 2^2x-3 — 2^2x-2 — 1 = 0
Found 4 solutions by greenestamps, mccravyedwin, ikleyn, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Assuming the equation is ....

Factor out of the first two terms:




The expression is always positive, so is always negative; then subtracting 1 makes the expression more negative. So the given expression is never equal to 0. In fact, it should be clear that the value of the expression is always less than -1.

A graph shows this:



ANSWER: no solution
Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!




let 

















There is no real solution.  Do you want complex solution(s)?

Normally if complex solutions are wanted, the variable is z, not x.

Edwin
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

One look at this equation is enough to see that it has no solutions in real numbers.

Indeed,  for any real value of  x,     is less than  .

So,  the difference   -  is always negative.

When you subtract  1  from this negative number,  you get negative number lesser than  -1.

Thus,  left side of the equation can not be equal to zero.



Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
But it does have a complex solution





let 

















Since  by one of many of Euler's equations.











Take natural logs of both sides:













Edwin
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