Question 207458
You do not need to know the base of the logarithm to figure out the domain. (The base is 10, by the way.) The domain is the set of all possible/allowable values for x.<br>
Since your equation has x in the argument of the logarithm (and nowhere else) we have to ask ourselves: "What are the allowable values for arguments to log functions?" If we understand logarithms we will know that the answer is: "Arguments to log functions must be positive (regardless of the base)." After all how can you raise 10 or 2 or "e" or 13 or whatever to a power and get zero or a negative number? Answer: You can't. (<i>Even negative exponents just result in <b>positive fractions</b>, not in negative numbers!</i>)
Since your argument is 2x - 12, then the domain is the set of x-values which make 2x - 12 positive. In other words:
2x - 12 > 0
The domain will be the solution to this inequality. To solve, add 12 to both sides:
2x > 12
And then divide both sides by 2:
x > 6
The domain, then, is all numbers greater than 6. In interval notation this would be: (6, {{{infinity}}}).