The question is:

State the domain of the function f(x) = log3 (x - 4)

I believe that the answer is all real number except 4.

Is this correct?

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- Dec 18th 2009, 12:15 PM #1

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- Dec 18th 2009, 12:29 PM #2

- Dec 18th 2009, 12:55 PM #3

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You have to remember that.....

$\displaystyle \log_a{b} = x \rightarrow a^{x} = b$

Then think about what $\displaystyle a^{x}$ will give me a negative number for b....none. You might think -1 or -2, but those are merely $\displaystyle a^{-1} = \frac{1}{a}$ and $\displaystyle a^{-2} = \frac{1}{a^{2}}$ and so on and so forth.

Similarly no x value will also give you 0, some might try zero, but $\displaystyle a^{0} = 1$

So you can see that the domain has to be restricted for positive values.

An easy way to find what values will work is

$\displaystyle x - 4 > 0$ and solve. Remember it cannot be 0 so it's a strict inequality.

If you are given numerous logs you can do the same for each and if you end up with a quadratic you can compare the solutions to see which fit the criteria.

Hopefully this helps.

- Dec 18th 2009, 01:11 PM #4

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