How to solve 2×exp(x)+2x-7=0 ?
#2e^(x)+2x-7=0#
2 Answers
We can solve this question graphically .
Explanation:
The given equation
Now take these two as separate functions
This is shown below :-
This one's beyond high school algebra, and the best way to solve it is to ask Wolfram Alpha who answers
Explanation:
Solve
Questions like this are in general hard, and the answer depends if you're in Algebra in high school or deeper into math.
For high school, the best approach is to just try some small numbers and see if they work. (This works for many, many high school math problems, fyi.) There is really only one rational
If an approximation is good enough, we can graph it, or graph
Whatever your level, when faced with a hard one like this, it's usually a good move to ask the available expert, which is Wolfram Alpha .
We see Alpha gave us an approximate answer, pretty close to 1, and even a formula using W(x), which the Lambert Product Log, which isn't usually part of high school math.
There's no answer using regular functions and operations we know about in high school Algebra. That's generally true when we add a term with
That's the end of the answer for most students. But we can go deeper. The product log is an interesting function. Consider the equation
On the right side is an increasing function of
We need something like a log, but not one that's the inverse of
We'll restrict our attention to the reals. It's fun to try to discover
Let's let
That's cool. How about
Taking logs,
Now that you see what it's like working with W, see if you can use it to solve the equation, or to check Alpha's solution