Solve for x.
Is there an algebraic solution for this? I plugged in values for , giving me what I suspect is right, x < 1. But how to be sure?
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Solve for x.
Is there an algebraic solution for this? I plugged in values for , giving me what I suspect is right, x < 1. But how to be sure?
@earboth
1. it would be much easier if he draw 3^x and 4x and find values where 4x is "bigger" then 3^x
2. I do not what made you think that if they're "monotically increasing there exists only one solution"?
example: x^3+5 and 3^x, both monotonically increasing but have 2 intersections.
Hello, rowe!
There is no algebraic solution, but there is a graphical solution.Quote:
Solve: .
We have: .
The question becomes: when is below ?
The graphs look like this:Code:
*  *
*
 * *
 o
 * : *
* : *
*  : *
*  : *
      +  +     *  
 1 *

As you pointed out, the curves intersect at
You answer is correct: .