Can x=-2 since we can change the equation into (1/x^2)=1/4 and therefore x^2=4 and if we take the square root of both side, x would equal 2 and -2?

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Hussain -A log function with a negative base will give you crazy results.Specifically, what is (-2) ^ (1/2) ?  This would result in an imaginary number!  So, the log would be undefined when the exponent equals 0.5.Mathematicians can't let that happen, so they require the base to be > 0 under real numbers.