How do you solve for x in #x+log_2x=6# ?
2 Answers
Explanation:
This is a transcendental equation since x is in the logarithm and not. Therefore, it does not in general have an easy solution and there isn't any perfect method for solving it.
This one does have a simple solution, but this is because this function had to be selected very carefully.
Let's assume there's some integer
Plugging in values of n,
So the solution
One cannot solve the equation
Explanation:
One can use a graphical method by converting the base to base
Convert to base
Subtract x from both sides:
Multiply both sides by
Separate into two equations:
Graph the two equations:
Please observe that the two graphs intersect at
You can use a recursive computation method such as Newton's Method to approximate the solution. Because the method requires many lines of computation, I will not do it, here, but I have provided a link so that you may read about it.
The easiest way to obtain a solution is to enter the original equation into WolframAlpha
Please open the above link and observe that WolframAlpha has computed the solution and it is