Alex R.
asked • 10/31/16What is log(BASE-1)(-1)
Is it 1 or is it 2x+1? There are a couple ways of solving it, either by change or base which will give you one, or converting it into exponential form which gives 2x+1. Which one is correct?
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1 Expert Answer
Kenneth S. answered • 10/31/16
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The base of a logarithm must be a positive number.
Alex R.
How come?
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10/31/16
Kenneth S.
bx with positive base can represent any Real number, for any Real x.
Examples: 100.30103 = 2, 10-0.30103 =½ using common logarithms (base 10).
If b=0, you can't get much out of that!
If b = -10, and x = ½, then you're trying to get square root of -10, and that's not a Real number.
These examples should serve to justify b>0 as requirement.
Then, too, you can take the inverse of y = bx which is y = logbx.
For exponential, x is any Real, y is any positive Real;
for logarithm, involving interchange of aforementioned x & y, the output y is any Real, the input x is any positive Real, but for both functions, b>0 is a requirement.
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10/31/16
Kenneth S.
Go back to Algebra II and review graphs of y = bx and y = logbx which are inverses of each other.
The base b has to be positive.
y = (-2)½ would be an attempt to take square root of -2, which is not Real. This single counterexample shows why base of an exponential (or logarithm) must be positive.
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10/31/16
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Mark M.
10/31/16