can ln be negative 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
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 Why can t logarithms be negative While the value of a logarithm itself can be positive or negative the base of the log function and the argument of the log function are a different story The argument of a log function can only take positive arguments
can ln be negative
can ln be negative
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The natural logarithm can be defined for any positive real number a as the area under the curve y 1 x from 1 to a with the area being negative when 0 a 1 The simplicity of this definition which is matched in many other formulas involving the natural logarithm leads to the term natural You can t have a negative amount of bacteria can you 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
The negative log of an argument is the logarithm of the reciprocal of the argument i e log b a log b a 1 log b 1 a The negative log with a base is the logarithm whose base is the reciprocal of the given base i e log b a log 1 b a 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
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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 base 1 Note 1 Remember property 1 The natural log of a negative value is undefined
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View Question Can You Apply A Ln To A Negative Number
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can ln be negative - You can t have a negative amount of bacteria can you 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