1. ## Nonlinear Equation

Is there an easy way to solve nonlinear equations such as

2^(x^3-4x) = (x - 1)

besides graphing?

Also how would you go about solving 16^(x+2) = 8^x

2. I’m not sure about the first equation, but the second equation can be solved by taking logarithm to base 2.

3. Originally Posted by BarlowBarlow1
Is there an easy way to solve nonlinear equations such as

2^(x^3-4x) = (x - 1)
There are numerical techniques, if you don't consider that to be graphing. I believe that you can also express the solution in terms of the Lambert W function, but this is technically an approximation as well.

-Dan

4. Hello, BarlowBarlow1!

Is there an easy way to solve nonlinear equations such as

$\displaystyle 2^{x^3-4x} \:= \: x - 1$ .besides graphing?
Well, the answer can be approximated by any of several available methods.

Solve: .$\displaystyle 16^{x+2} \:= \:8^x$

We have: .$\displaystyle (2^4)^{x+2} \:=\:(2^3)^x\quad\Rightarrow\quad2^{4x+8} \:=\:2^{3x}$

Therefore: .$\displaystyle 4x + 8 \:=\:3x\quad\Rightarrow\quad x \:=\:-8$