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## Q. 3.2.7

Finding the Domain of a Logarithmic Function

Find the domain of $f(x)=\log _4(x+3)$.

## Verified Solution

The domain of f consists of all x for which x + 3 > 0. Solving this inequality for x, we obtain x > -3. Thus, the domain of f is (-3, ∞). This is illustrated in Figure 3.13. The vertical asymptote is x = -3 and all points on the graph of f have x-coordinates that are greater than -3.