can log base be negative It s not that the base can t be negative it s that you lose the ability to guarantee your answers are consistent and real once you do To give a different example think of the input function to the function f x log 2 x f x log 2 x when x 8 x 8
Logarithms are actually decently complex functions Consider log 4 base negative two This is equivalent to log4 log 2 When you allow logs to have negative arguments then you re dealing with complex numbers and the logarithm becomes a multi valued function Negative bases When the base is negative and the exponent is rational with an odd denominator like 64 1 3 there is a negative real number 4 which can be chosen to be the principal value When the base is negative and the exponent is rational with an even denominator there is no real root
can log base be negative
can log base be negative
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Why We Cannot Evaluate The Logarithm Of Zero Or A Negative Number if
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Logarithmic Functions
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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 No that s not right no matter what the base b b logb x log b x is not defined for x 0 x 0 Recall that logb x y log b x y means that by x b y x If b 0 b 0 and b 1 b 1 no power of b b is negative or 0 0 so the equation by x b y x has no solution for x 0 x 0
The Natural Log Rules Explained In math log rules also known as logarithm rules are a set of rules or laws that you can use whenever you have to simplify a math expression containing logarithms Basically log rules are a useful tool that when used correctly make logarithms and logarithmic equations simpler and easier to work with when solving problems The tricky thing about negative base logarithms is that unless you re prepared for them to be complex valued the set of values they can take isn t continuous For example what s log 2 3 Well unfortunately no real x solves 2 x 3 in fact x 2 x can only both be real if x is a rational number which in its lowest
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The base of a logarithm cannot be negative because a negative base raised to a fraction only has an imaginary solution A base of 0 would always result in 0 since 0 raised to anything is 0 and a base of 1 will always result in 1 The answer is basically yes but it s not generally very useful First let s look at logarithms with positive bases If a 0 and a 1 then ax 0 R is a one one function with inverse loga R 0
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can log base be negative - No that s not right no matter what the base b b logb x log b x is not defined for x 0 x 0 Recall that logb x y log b x y means that by x b y x If b 0 b 0 and b 1 b 1 no power of b b is negative or 0 0 so the equation by x b y x has no solution for x 0 x 0