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Chapter 4: Problem 78

Find the domain of each logarithmic function. $$f(x)=\log (7-x)$$

Short Answer

Expert verified
The domain of the logarithmic function \(f(x) = \log (7-x)\) is \(x < 7\).

Step by step solution

01

Identify the argument of the logarithmic function

The argument of the logarithmic function \(f(x) = \log (7-x)\) is \(7-x\).
02

Set up inequality

Because the argument of a logarithm has to be greater than 0, we have the inequality \(7-x > 0\).
03

Solve the inequality

To solve the inequality \(7-x > 0\), we will isolate x on one side by adding x to both sides and subtracting 0 from both sides, which yields \(x < 7\).

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Most popular questions from this chapter

Would you prefer that your salary be modeled exponentially or logarithmically? Explain your answer.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { The domain of } f(x)=\log _{2} x \text { is }(-\infty, \infty)$$.

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$\log (x-15)+\log x=2$$

Explain how to find the domain of a logarithmic function.

Without using a calculator, find the exact value of $$\frac{\log _{3} 81-\log _{\pi} 1}{\log _{2 \sqrt{2}} 8-\log 0.001}$$
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