Expert: Richard J. Raridon - 3/29/2010

Question
QUESTION: Just by observation, I know that x = 3 in the following:  (x + 1)/(2^x) = 1/2  

Multiplying both sides of the equation by (2^x) will get (x + 1) = 2^(x-1)  I just don't know if this is the correct direction I need to go to solve for x.  I'm stuck.  Can you help me with solving for x mathematically?


Thanks

ANSWER: If you multiply both sides by 2^x you get x+1 = (1/2)2^x, not what you got.  Or 2^x = 2(x+1)
I don't know of an easy way to solve for x other than trial and error which will lead to your answer of 3.  

---------- FOLLOW-UP ----------

QUESTION: The original equation is (x+1)/(2^x) = 1/2
Multiplying both sides by 2^x gets me (x+1) = 2^(x-1) which is a similar form to what you get.  Here is how I got it: 1/2 = 2^(-1) therefore the right side of the equation is (2^x)(2^(-1)) or 2^(x-1)

I have never come across an algebra problem that requires a simple solution to be derrived by trial and error.  I know the answer is x=3, but I cannot solve it mathematically!

Answer
Okay, I hadn't looked at it close enough to see that both equations lead to the same solution.  
There are lots of problems that require trial and error.  For example, f(x) = x^3+3x^2-2x-5
That can't be factored so you just have to put in values for x and calculate f(x).
so f(0) = -5, f(1) = -3 and f(2) = 11.  Therefore, there's a solution between x=1 and x=2.  
Then try f(3/2) to get 17/8, f(5/4) = -55/64.  Now you know the solution is between x=5/4 and
x=3/2.  You can narrow it down as far as you want.