Find the domain of $f(x)=\ln(3x+2)$ 
Find the domain of $f(x)=\ln(3x+2)$

I can find domain, but is it the same for a $\log$ function? And also, do I have to rid the equation of the $\ln$ before I can find the domain? I'm really confused as to how to start out this problem. Please help.
Edit: I got the answer and now I ask a question (irrelevant to my problem but I am curious), why does the real portion of $f(x)=\log x$ resemble the graph of a square root function. In a sense of, starting at a single point and going in two directions: up/down & left/right.
 A: Hint: $\log t$ is defined precisely if $t$ is positive. The base is irrelevant.
Why: The explanation depends on how you define the logarithm. Let $b\gt 0$, with $b\ne 1$. Then $\log_b t$ can be defined as the number $w$ such that $b^w=t$. But $b^w$ is always positive, so $t$ must be positive. Thus $\log_b t$ is undefined if $t \le 0$. 
To show that $\log_b t$ is defined whenever $t\gt 0$, we need some information about the function $b^w$. Assume that $b\gt 1$. Then $b^w$ is steadily increasing, and is close to $0$ when $w$ is large negative, and is huge when $w$ is large positive. Thus the function $b^w$ takes on every positive value once and only once. A similar argument settles the (much less common) situation where $0\lt b\lt 1$.  
A: What is the domain of $g(t)=\ln(t)$? For which $x$ is $3x+2$ in this domain? There's no need to remove the logarithm first.
A: As this is tagged pre-calculus, I'll assume that you want $y=f(x)$ to be a real number. The first step is: where is $\log x$ undefined? Then, when you answer that question, you can adjust that domain for the transform $x \to 3x+2$.
A: $log_a (b)=c$ if and only if $a^c = b$, where $a>0$. Since $a$ is positive, $b$ will also be positive since a positive number to a real exponent will always be positive. Therefore, the  expression in the logarithm will always be greater than zero. In your case, this simplifies to $3x+2>0$. Solve for $x$ to get $x>-\frac{2}{3}$. Thus, your domain is $(-2/3, \infty)$.
