I can't find the log of a negative number

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SUMMARY

The equation 2x = -6 has no solution in the realm of real numbers. This is due to the fact that a positive base raised to any real exponent cannot yield a negative result. Therefore, the conclusion is that the logarithm of a negative number is undefined in this context, confirming that the problem may contain a typographical error or is part of a larger, unsolvable equation.

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Homework Statement


there is an equation:

2^x=-6


Homework Equations





The Attempt at a Solution


I know that log need to be used to find x. but I can't find the log of a negative number,,
 
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AllenHe said:

Homework Statement


there is an equation:

2^x=-6


Homework Equations





The Attempt at a Solution


I know that log need to be used to find x. but I can't find the log of a negative number,,

And you cannot raise a positive number base to any real number exponent to get a negative power. So the answer is "no solution," unless the problem is a typo. Or, was this a part of a larger problem?
 

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