+129849 Why is it not possible to solve log(x, -3)= ?
I'm not familiar with this notation, but we can't take a log of a negative number, nor can we use a negative number as a log base - if this is what you're asking???
To see the first one, suppose I had log (-23). In exponential terms, I want to know what exponent I can append to 10 to give me -23. Answer......there is none. 10 raised to any power is a positive number.
To see the second one, suppose we used (-10) as a base. Now, suppose I wanted to find log-10 10.
This says, in exponential form, what power do I put on (-10) to raise it to 10?? Answer..... there is none.
Note (-10)^0 = 1 but (-10)^1 = -10 and (-10)^2 = 100. Note how the answers "oscillate" back and forth. In other words, (-10) raised to 0 is actually greater than (-10) raised to the next integer power !!!! Notice also, that (-10)^3 would, again, be negative (-1000) - and less than (-10)^2 !!!!
Thus, we can't use a negative number as a log base, and we can't take the log of a negative number (or "0,"
either !!!).........I hope this answers your question.......
+6251 Everything CPhill says is entirely correct. For the the real numbers.
Things are different with complex numbers and the Log function becomes rather complicated in that it becomes "multivalued" and it's domain must be restricted in order to make it a proper function.
This leads to the concepts of branch cuts and Riemann surfaces and it gets sophisticated pretty quickly.
