Why is y=log x^2 and y= 2 log x different when graphed?

Question

Can you explain to me why y= log x^2 and y=2 log x are suppose to be similar, yet when you graph them they are slightly different.

Can you tell me why it occurs?

Thanks

Hustolemyname - answer to your question is yes.

Answer 1

The property "log (a^b) = b log a" holds only when a is a positive number.

If a is negative, then log a^b may be defined even if b log a is not. For example, log ((-e)^2) = log (e^2) = 2, but 2 log (-e) is not defined (at least, in the real numbers).

y = log (x^2) and y = 2 log x should agree for positive numbers. The function y = log (x^2) will also have values for negative x, whereas the function y = 2 log x will not.

As a previous answerer pointed out, the graphs of y = log(x^2) and y = 2 log |x| should agree.

Answer 2

I agree with maussy

in y = log x^2 the calculator is probably looking up the log of an integer or at least the log of a finite decimal.

in y=2 log x the calculator is doubling an irrational number which it will have to do by approximating it first.

Answer 3

in case you do this on a crap calculator and it sounds such as you're you log(x-2)/log(2) and a pair of-log(x)/log(2) in any different case use a graphing calc they at the instant are not extraordinarily diverse one is the different way up and shifted on the y axis and the different is shifted on the x axis.

Answer 4

they are different. x must >0 when y= 2 log x
y= log x^2 and y=2 log |x| are the same

Answer 5

Hi:
You should notice that the domain of the first function is R without zero but the domain of the second one is non zero positive numbers.
regards

Answer 6

you are graphing log(x^2) and not (log(x))^2 aren't you?

Answer 7

It should be the same

perhaps the calculator makes errors in rouding