why can t ln be negative Assume we do have logarithms for negative numbers and zero and all the properties of logarithms are preserved Then we immediately obtain a contradiction Here it is 0 log 1 log 1 2 2 log 1 so log 1 0 and from the definition of logarithms we have
Ln of a Negative Number The ln of a negative number is undefined ln of 0 ln 0 is undefined ln of 1 ln 1 0 ln of Infinity ln ln of e ln e 1 ln of e raised to the x power ln e x x e raised to the ln power e ln x x At most er least you can have zero but there s no way to have a negative amount of the little critters Negative bacteria just doesn t make sense ln text negative number text undefined Undefined just means there is no amount of time you can wait to get a negative amount
why can t ln be negative
why can t ln be negative
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Negative numbers and the number 0 aren t acceptable arguments to plug into a logarithm The only numbers you can plug into a logarithm are positive numbers You are correct that when x 8 the expression x 4 becomes negative which is not valid because the logarithm of a negative number is undefined However you should keep both answers 8 and 4 and check them separately to
Did your teacher tell you you can t take the log of a negative number Well that s only true if you restrict yourself to logarithms that are real numbers If you allow for complex numbers then you can take the log of a negative or complex number To find such logarithms say log 5 6i you need to put the number in polar form first Why can t logarithms be negative While the value of a logarithm can be a negative number the argument x value of any logarithm cannot be negative This is because the base of a logarithm can only be a positive number greater than 1 and a positive number raised to anything will be a positive number
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If the base of the logarithm is negative then the function is not continuous For instance sure the logarithm is defined for even and odd powers of negative numbers though even powers are positive and the odd powers a negative and this is a wild jumping behavior that will continue for all integers However what about values between the Q2 the base must be positive because when we rewrite a logarithmic expression with a negative base using the base swap rule we will be putting a negative value through log example log 8 log 8 log 2 you cannot log a negative value because it would be like trying to find a base 2 with a negative value noo
Descriptions of Logarithm Rules Rule 1 Product Rule The logarithm of the product is the sum of the logarithms of the factors Rule 2 Quotient Rule The logarithm of the ratio of two quantities is the logarithm of the numerator minus the Given a logarithm is true if and only if y log b x and b y x and x and b are positive and b is not equal to 1 are true why aren t logarithms defined for negative numbers Why can t b be negative Take 2 3 8 for example
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why can t ln be negative - Why can t logarithms be negative While the value of a logarithm can be a negative number the argument x value of any logarithm cannot be negative This is because the base of a logarithm can only be a positive number greater than 1 and a positive number raised to anything will be a positive number