![negative logs negative logs](http://jwilson.coe.uga.edu/EMAT6680Su10/Spooner/Assignment1KS/alogpos.gif)
Then what we know is that, if the base of our power function is positive, it doesn’t matter what exponent we put on that base (it could be a positive number, a negative number, or 0), that power function is going to come out as a positive number. And if those numbers can’t reliably be the base of a power function, then they also can’t reliably be the base of a logarithm.įor that reason, we only allow positive numbers other than 1 as the base of the logarithm. And after solving several problems, I noticed - all numbers that are put into the. So when people saw they were in the A-Level syllabus, many said 'I hate logs' immediately after looking at the list of log rules. Logs was always one of the less popular, less well-known topics at GCSE. Logarithms of numbers between 0 and 1 are NEGATIVE if the base is more than one. I found myself asking this question after studying logarithms in school. So 0, 1, and every negative number presents a potential problem as the base of a power function. Logarithms of negative numbers are not defined. And as you know, unless we’re getting into imaginary numbers, we can’t deal with a negative number underneath a square root.
![negative logs negative logs](http://www.originlab.com/ftp/forum_and_kbase/Images/matlab_negative_logscale_plot.png)
If you raise a negative number to a positive number that’s not an integer, but instead a fraction or a decimal, you might end up with a negative number underneath a square root. In the same way, 1 raised to anything is always still 1. Or, put a different way, 0 raised to anything is always still 0. In other words, there’s no exponent you can put on 0 that won’t give you back a value of 0. When you have a power function with base 0, the result of that power function is always going to be 0. To understand why, we have to understand that logarithms are actually like exponents: the base of a logarithm is also the base of a power function. The reason has more to do with the base of the logarithm than with the argument of the logarithm. Negative numbers, and the number 0, aren’t acceptable arguments to plug into a logarithm, but why? In other words, the only numbers you can plug into a log function are positive numbers. The argument of a log function can only take positive arguments. 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.