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Actually, it is possible - if you calculate with complex numbers.

In the real numbers... Let's see an example.

Asking for x = log101000 (the base may be assumed, but I will include it here for clarity) is like asking: 10x = 1000. Clearly, the solution is 3.

Asking for x = log100.001 is the same as asking 10x = 0.001; the solution is -3.

But asking for x = log10(-1) is like asking 10x = -1. This doesn't have any solution; for positive values of "x" the right side (the result of taking the power) will be more than 1, for negative values of "x", the right side will be less than 1, but always more than zerowill. If x approaches minus infinity, the result of the power will approach zero - but it will never reach zero, nor will it be less than zero. Do some powers on your calculator to help you visualize this.

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Q: Why a lograthims of negative number is not possible?
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