I can't find the log of a negative number

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The equation 2^x = -6 cannot be solved using real numbers because a positive base raised to any real exponent cannot yield a negative result. Consequently, there is no solution to the equation. The discussion raises the possibility of a typo in the problem statement. Without additional context or modifications, the conclusion remains that the equation has no valid solution. Thus, the issue centers on the impossibility of logarithmic calculations involving negative numbers in this scenario.
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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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