Negative Value Equated to Exponential Expression

This is a very interesting maths question, that may trick many students.

2^x = -1

What is the value for x?

I got all sort of answers.
Some gave me x = 0 (knowing that 1 = anything to the power of 0).
Some treat the expression to be 2x = -1 ==> x = -1/2.
Some used the calculator, applying "logarithm" operation and getting an "Error" message!

Those who know the answer, congratulation. You can stop reading this post.

For those interested and wanting to know what's the answer, read on...

Knowing the answer, is fine here. But knowing with understanding is better.

Now, let's put some numerical values of x into the expression.

If we choose x = +3, y = 2³ = 8 ( a positive number).
If we choose x = -3, y = 2^-3 = 1/8 ( a positive number).
If we choose x = 0, y = 1 (again a positive number).

Conclusion: All the x values substituted will get us positive number instead of the desired negative number.

Then how do we get a NEGATIVE number from the exponential expression?

The answer is:
WE can NEVER get a valid numerical value for x for expression in the form a^x or equivalent when it is equated to a negative value.

Clear?
Do not fall into this mathematical trap. You will not look good, if you can solve it!

Have fun testing your classmate.

:-)