We will present that the logarithm the a negative number or zero is unknown or does no exist.

Similarly, girlfriend cannot discover the logarithm that the complying with expressions.

log5 -125     

log10 -100                    

log5 0                

log4 0

Why the logarithm that a an unfavorable number cannot be negative?




You are watching: Can you take the log of a negative number

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The reason for this is that any type of positive number b increased to any power x cannot equal to a number y less than or equal to zero.The definition says If y = bx, then logb y = x

If x is bigger 보다 zero or x is same to zero, that is apparent that bx will be bigger than zero together you can see in the examples below. As a result, y will likewise be bigger 보다 zero because y = bx650 = 1

70  = 1241 = 2423 = 842 = 1653 = 125

64  =129685 = 32768

How about when x is negative?  Let x  = -2, -3, and -8 and let b = 5y = 5-2 = 1 / 52 = 1 / 25 = 0.04

y = 5-3 = 1 / 53 = 1 / 125 = 0.008

y = 5-8 = 1 / 58 = 1 / 390625 = 0.00000256


As you can see, return y can acquire very tiny or very close to zero, that will never ever be equal to zero or worse it is in a negative number. That is the key concept here!


Since y have the right to never be zero or negative, the does not make feeling to change y inlogb y with zero or a an adverse number.Now, girlfriend can plainly see why this expressions perform not do sense

log5 -125                       log10 -100                     log5 0                 log4 0

In fact, for log5 -125, there is no number x, such 5x = -125If you choose 3, girlfriend will acquire 53 = 125 and also if you select -3, girlfriend will acquire 5-3 = 0.008If the did not work for x = 3 and x = -3, no other numbers will work!

By the same token, for log5 0, there is no number x such the 5x = 0


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