Since (-x)^2=(x)^2, we have log (-x)^2=log(x)^2, whence 2 log(-x)=2 log (x), and thence log (-x)=log(x).
What in the world does this mean????
2007-07-30 13:18:00 · 5 answers · asked by Mike 2 in Science & Mathematics ➔ Mathematics
It means you get in trouble when you try to take the log of a negative number.
2007-07-30 13:21:25 · answer #1 · answered by Anonymous · 1⤊ 0⤋
This assumes that log (x^2)=2*log(x), which is correct if x>0
and that log((-x)^2)=2*log(-x), which is correct if -x>0
Of course, -x and x cannot both be greater than than 0.
Here is something easier to understand that is based on the same concept but does not involve logs:
x*x=x^2
(-x)*(-x)=(-1*x)*(-1*x)=(-1*-1)*(x*x)=(1)*(x^2)=x^2
-x*-x=x*x
(-x)^2=x^2
This is correct, but if you took the square root of each side of the equation, you would get (-x)=(x), which is not.
2007-07-30 20:31:15 · answer #2 · answered by StephenWeinstein 7 · 1⤊ 0⤋
(-x)^2 = (x)^2 ...... because minus *minus is +
then log (x)^2 = log (-x)^2, and one logarithms law says that log(x)^2 = 2 log(x) ; and log(-x)^2 = 2 log (-x) then according to Bernoulli theory:
log(x) =log(-x) Check what Bernoulli says about logarithms of negative numbers.
2007-07-30 20:38:55 · answer #3 · answered by mimi 3 · 0⤊ 0⤋
The log of a negative number is undefined. Your logic is fine until you take the step 2log(-x) = 2log(x).
2007-07-30 20:29:10 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋
OH Bananas, what is that!
2007-07-30 20:31:07 · answer #5 · answered by Anonymous · 0⤊ 1⤋