2^((-2)^x) =x how do you solve for x? without a calculator?

[hangainlover]

I thouht about derivatives of both sides.
But it leaves me with a negative number inside ln...
I can't think of any way to solve it without a calculator
help?

 

[arildno]

I thouht about derivatives of both sides.
But it leaves me with a negative number inside ln...
I can't think of any way to solve it without a calculator
help?

It can't be done exactly, in a finite number of steps.

 

[HallsofIvy]

I thouht about derivatives of both sides.
But it leaves me with a negative number inside ln...
I can't think of any way to solve it without a calculator
help?

The first thing you will have to do is define $(-2)^x$. A negative number to most irrational powers is not defined.

 

[disregardthat]

The first thing you will have to do is define $(-2)^x$. A negative number to most irrational powers is not defined.

In the complex range however they have a natural definition.

 

[TylerH]

I don't think a calculator's going to help much either. My TI-89, with command "solve(2^((-2)^x,x)", returns "false". :)

 

[cubzar]

2^((-2)^x)=x
log2((-2)^x)-log2(x)=0
log2(((-2)^x)/x)=0
((-2)^x)/x=1
x=(-2)^x
2^x=(-2)^x=x
I don't know how to proceed.