SOLUTION: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2 The answer is -1, 1. Please explain and show to me how to get the answer. pls.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2 The answer is -1, 1. Please explain and show to me how to get the answer. pls.      Log On


   

Question 1035074: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2
The answer is -1, 1. Please explain and show to me how to get the answer. pls.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
2^(1+2x)-5(2x)=-2

2%5E%281%2B2x%29-5%282x%29=-2
%282%5E1%29%282%5E%282x%29%29-5%2A2x=-2
2%282%5E%282x%29%29-10x=-2
2%5E%282x%29-5x=-1
No clear simple algebraic way to solve from here. x in an exponent and x in a term without exponents.


You might arrange as 2%5E%282x%29=5x-1 and make a graph of left side and right side both as functions of x, and identify the intersection.

You say that the answer is supposed to be -1. Check to see if this value works in the equation.
CHECKING: 2%5E%282%28-1%29%29-5%28-1%29=-1
2%5E%28-2%29%2B5=-1
1%2F2%2B5=-1
5%261%2F2=-1
cross%285%261%2F2=-1%29
The reported answer DOES NOT WORK as a solution.

Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given function is 2(raise to the power of 1+2x) - 5(2x)= -2
The answer is -1, 1. Please explain and show to me how to get the answer. pls.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1. (-1) is not the root.

2. 1 is the root.

3. There is one more positive root at x ~ 0.9.

4. It may be proved mathematically that there are only two roots, using convexity, for example.

5. The second root might be found approximately/numerically by applying some iteration process.

   Or graphically.

6. I do not see a way to find the second root analytically by means of school math.



Figure. Plot y = 2%5E%281%2B2x%29+-+10x+%2B+2.