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[tex]P= log_x(Q)[/tex] is equivalent to [tex]Q= x^P[/tex]. How, exactly, would you define [tex]x^{-1}[/tex] if x were equal to 0? How would you define [tex]x^{1/2}[/tex] if x were -1? In order that we not have to give special definitions to cases like those, we only define the exponential for positive base. And from that, logarithm can only be defined for positive base.roni said:
A logarithm is a mathematical function that represents the inverse of an exponential function. It is used to solve for an unknown in an exponential equation.
In the limited logarithm, the base is restricted to be greater than 1. If x is less than or equal to 0, then the logarithm would result in a negative number, which is not defined in this case.
No, the limited logarithm is only defined for positive numbers. This is because the base of the logarithm must be greater than 1, and negative numbers cannot be raised to a power to result in a positive number.
The limited logarithm is a special case of the standard logarithm, where the base is restricted to be greater than 1. The standard logarithm, on the other hand, can have any positive base.
The limited logarithm is commonly used in finance, biology, and physics to model exponential growth and decay. It is also used in computer science and information theory.
