2^x = 2x+1

Solve for x

Question

2^x = 2x+1

Solve for x

mhchen · Answer

Looking at a graph, 2^x intersects 2x+1 at x=0 and x=2.66...
but how would I solve this algebraically? I can't figure out how to get x by itself.

dude · Answer

Use logs

mhchen · Answer

$$\log_{2}{2x+1} = x $$
Now what

nuts · Answer

Why do you assume you can solve it algebraically?

mhchen · Answer

Is it not possible to solve algebraically?

nuts · Answer

I don't think so, and even if you could, the solution to something like this would involve the use of special functions like the lambert W function.

mhchen · Answer

Dam...I looked on other websites and they also used the lambert W. I guess you're right, I can't do this. ;\ I'll ask my teacher about it.

nuts · Answer

Now the question of WHETHER or not you can solve it, is a much deeper question that comes down to field theory and is probably way beyond the scope of any undergraduate level mathematics course.