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

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In summary, the conversation discusses trying to solve a problem involving derivatives and a negative number inside ln without a calculator. However, it is mentioned that it cannot be solved exactly and requires a definition for (-2)^x in the complex range. The conversation also mentions using a calculator, but it is not helpful in finding a solution.
  • #1
hangainlover
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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?
 
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  • #2
hangainlover said:
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. :smile:
 
  • #3
hangainlover said:
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 [itex](-2)^x[/itex]. A negative number to most irrational powers is not defined.
 
  • #4
HallsofIvy said:
The first thing you will have to do is define [itex](-2)^x[/itex]. A negative number to most irrational powers is not defined.

In the complex range however they have a natural definition.
 
  • #5
I don't think a calculator's going to help much either. My TI-89, with command "solve(2^((-2)^x,x)", returns "false". :)
 
  • #6
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.
 

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

What is the first step in solving this equation?

The first step is to isolate the exponent on one side of the equation. In this case, we want to move the x term to the right side.

How do you isolate the exponent?

To isolate the exponent, we can take the logarithm of both sides of the equation. This will allow us to bring the exponent down as a coefficient.

What is the next step after taking the logarithm?

Next, we can use the power rule of logarithms to bring the exponent down as a coefficient. This will result in a linear equation that can be solved for x.

How do you solve the linear equation for x?

To solve the linear equation, we can use algebraic techniques such as combining like terms and isolating the x term on one side of the equation. Once the x term is isolated, we can solve for x by dividing both sides by the coefficient.

Is it possible to solve this equation without a calculator?

Yes, it is possible to solve this equation without a calculator using algebraic techniques. However, the resulting value of x may be difficult to determine without a calculator as it may involve decimal or irrational numbers.

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