Little ant
- 21
- 0
Find the solutions of 5^x=2x+1 by ordinary methods? if it can´t be found by these ways, then prove that it's imposible.
Solve 5^x=2x+1 or Prove Impossibility
- Context: Undergrad
- Thread starter Little ant
- Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
4 replies · 2K views
Discussion
stevenb
- 701
- 6
It depends on what you mean by ordinary methods.
By inspection, x=0.
By inspection, x=0.
Little ant
- 21
- 0
but, there is other answer, how you find it?
Femme_physics
Gold Member
- 2,548
- 1
The exponent ^5 is behind the X or after?
JJacquelin
- 801
- 35
Ordinary method consists in studying the function y=(5^x)-(2x+1)
This shows that two roots exist (one of them is obvious).
Drawing the graph of the function allows to obtain a first approximate of the second root.
Then, numerical computation leads to the value of the root, as accurate as we want. There are a lot of numerical methods : Newton-Raphson and many other...
Analytical solving is outside the scope of ordinary methods. It requires the use of a special function : the Lambert W function.
This shows that two roots exist (one of them is obvious).
Drawing the graph of the function allows to obtain a first approximate of the second root.
Then, numerical computation leads to the value of the root, as accurate as we want. There are a lot of numerical methods : Newton-Raphson and many other...
Analytical solving is outside the scope of ordinary methods. It requires the use of a special function : the Lambert W function.
