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

## Main Question or Discussion Point

I thouht about derivatives of both sides.
But it leaves me with a negative number inside ln....
I cant think of any way to solve it without a calculator
help?

arildno
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I thouht about derivatives of both sides.
But it leaves me with a negative number inside ln....
I cant think of any way to solve it without a calculator
help?
It can't be done exactly, in a finite number of steps. HallsofIvy
Homework Helper
I thouht about derivatives of both sides.
But it leaves me with a negative number inside ln....
I cant 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.

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

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.