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I'm taking pre-calc and I'm already falling behind this semester.

I'm hoping someone could give me a simple explanation on how to solve these types of problems:

$$f(x) = \log_5(4-x^2)$$

I have the answer, but I don't know how to get to it exactly.

I think I factor whatever is inside of the log. But then what's the point of the log?

Here's a few more problems that are similar:

$$f(x) = \log(x^2 - 13x + 36)$$

$$f(x) = \ln|7 + 28x|$$

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    Logarithm is defined just on POSITIVE reals..2012-09-26
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    this is just a clever ruse to make you do an inequality of some expression of x and then see what inequality that implies about x2012-09-26
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    You wrote "these types of problems", followed by $f(x)=\log_5(4-x^2)$. But "$f(x)=\log_5(4-x^2)$" doesn't state any problem. If there's something above that that says "Simplify the following", then you'd have stated a math problem. If there's something above that that says "Find the domains of the following functions", then you'd have stated a DIFFERENT math problem. And if there's something above that says something else, you'd have yet another math problem. Before anyone can be sure what problem you're asking about, you need to give us that additional information.2012-09-26
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    Sorry about that Michael. I thought it was clear enough that the title explained what the problem was: "Analytically find the domain of a logarithmic function?". That's all the instructions on the paper.2012-09-26

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