# 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?

Homework Helper
Gold Member
Dearly Missed
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.

Homework Helper
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.

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.