SOLUTION: "SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS" ---> why is it that when any value of X results in a log of a negative number, it must be rejected??? it's from a workbook that

Question 34700: "SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS" ---> why is it that when any value of X results in a log of a negative number, it must be rejected???
it's from a workbook that my professor created - not a textbook.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Consider an example log (-10) = x
The exponential meaning of this is
10^x=-10
But no power of 10 can produce a negative number.
Oh?
What if we make the base -10 ?
Then (-10)^1 = -10
so, -10 works for this case; but what about (-10)^(1/2).
That is imaginary.
Negative bases just don't give the properties that log
functions need.
So the base must be positive and its powers can never be negative.
Cheers,
Stan H.

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