Why we don't use negative base in logarithm?
...But consider this:
(-2)^x = 3.
What's x? That is, what power of -2 could give you 3?
You'll either have no answer, or you'll say that it should be the same as the power of 2 that would give you 3.
But that power would be fractional.
And that, is a problem, because a fractional power of a negative number may not be a real number.
(-2)^x = 3.
What's x? That is, what power of -2 could give you 3?
You'll either have no answer, or you'll say that it should be the same as the power of 2 that would give you 3.
But that power would be fractional.
And that, is a problem, because a fractional power of a negative number may not be a real number.
The square root (that is, the 0.5-th power) of -1 isn't real (it's called iota, and an imaginary number), and this should be intuitively understand-able, that no real number on multiplying it by itself could possibly give a negative real number, since - * - = +, and + * + = +.
So is the case with other fractional powers of negative numbers.
The logarithms of non-simple numbers to a negative base can't be defined real-ly, so. Yeah. We just take them out of the equation altogether.
If you still don't get it, comment below.
The logarithms of non-simple numbers to a negative base can't be defined real-ly, so. Yeah. We just take them out of the equation altogether.
If you still don't get it, comment below.
Thanks
I understand it clearly
Answers
Answered by
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log of negative base is not defined.
it is due to if you will notice the graph of log x when its value on x axis does not crosses the origin in the negative side therefore it is not defined for the negative base
it is due to if you will notice the graph of log x when its value on x axis does not crosses the origin in the negative side therefore it is not defined for the negative base
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but we can write (-2)^3,then we say log-2 (-8)= -3 undefined ?
log-2 (-8)=3*
the domain of logarithm doesn't allow negative value in its base you can check the graph
thanks
Answered by
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Answer:
Step-by-step explanation:
the logarithm function is defined Only for strictly positive numbers.
my ques is why it is undefined?
Think of square root of x which is Only defined for x >= 0. this is the same. there are some functions that are Only defined for positive numbers. however in the complex plane u can use negative numbers
thanks a lot
Similar questions
By definition, you'd know that a^b = c, implies log of c to the base a is b.
Now, if a were negative, say (by your example, if you don't mind) -2, (-2)^b = c, implies log of c to the base (-2) is b.
But consider these:
(-2)^2 = 4. (2)^2 = 4.
Okay, it isn't a major problem...