Expert: Scott A Wilson - 7/3/2010

Question
I know from trail and error that x = 3 in the following equation:  (x+1)/(2^x) = 1/2    I tried to solve this equation several times using my knowledge of algebra, but I always get stuck in the process.  The question is: How can this problem be solved mathematically?

Answer
I don't know of how to solve it the way it is with basic math, however...

If the equation (x+1)/2^x = 1/2 is rearranged, it is 2(x+1) = 2^x.
Taking the log base 2 gives log(2) + log(x+1) = x * log(2).
Now log(2) = 1, since this is the log base 2, so this is 1 + log(x+1) = x.
This transforms to log(x+1) = x-1.

Plotting this makes it clear that x=3 should be tried.

Note that log(3+1)=log(4)=log(2^2)=2, since the log is in base 2.
Note that 3-1 = 2, and this is the same, so the answer is x=3.