posted by kristie on .
How do you find the domain of log(x^2-4)?
and how about this one? e^(3x+4)?
Please help me!
Well kristie, you might recognize log(x^2-4) = log((x-2)(x+2)) and then use a property of logs to see it as a sum, i.e., log(ab)=log(a)+log(b). You are then expected to know that the log function is only defined for positve values. Thus you only want x values that make the argument positive.
For the second you want the values that e^y is defined, where y = 3x+4. What values can an exponent be?
I get the first one, but I'm still a little confused about the second one. I thought an exponent could be any values. So would that make (-infinity, _infinity)?
yes, I think you understand it. Exponents can assume any values.
Just beware of a number with a fractional exponent, such as e^(1/(x-1)) for example. Here you need to restrict x not equal 1.