Why logarithms cannot be negative

How about when x is negative? As you can see, although y can get very small or very close to zero, it will never be equal to zero or worse be a negative number. That is the key concept here! Since y can never be zero or negative, it does not make sense to replace y in log b y with zero or a negative number.

Now, you can clearly see why these expressions do not make sense. Exponential and logarithmic functions.

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Everything you need to prepare for an important exam! K tests, GED math test, basic math tests, geometry tests, algebra tests. The base of the log is the base of the exponent function. Observe the result on the left. Well, we know that 0 raised to any power is still 0. Now let's imagine the base is 1 i. Again, just like last time, 1 raised to any power is just 1. So again, no matter what value x takes, y cannot be determined. This means the base cannot be 1. But then I realised - log base 1 of 1 can, in fact, be any number.

As we established earlier, 1 raised to any power gives 1. So, technically y can take ANY number. The base CAN be greater than 1 though, e. This wouldn't give us any real solutions!

Putting together all 3 conclusions, we can say that the base of a logarithm can only be positive numbers greater than 1.

Hence, negative bases for log cannot be used. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?

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