A fraction is undefined if the denominator = 0; obviuosly...
Are there values that when you take the natural log, the result is undefined?
Are there values, say x, such that e^x is undefined?
What are they? Thanks.
A fraction is undefined if the denominator = 0; obviuosly...
Are there values that when you take the natural log, the result is undefined?
Are there values, say x, such that e^x is undefined?
What are they? Thanks.
I'm afraid that's not a very good excuse. Let's try graphical explanation instead.
$\displaystyle \,e^x$
http://upload.wikimedia.org/wikipedi...px-Exp.svg.png
$\displaystyle \,\log_2(x)$
http://upload.wikimedia.org/wikipedi...rithm_plot.png
See it?
What you want to know is the domains of those functions- and you should learn that when you learn the functions.
The domain of ln(x) is "all positive real numbers" and so ln(x) is (literally) undefined for 0 or any negative numbers.
The domain of $\displaystyle e^x$ is "all real numbers" so $\displaystyle e^x$ is defined for all real numbers.