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Chapter 5: Q 84. (page 309)

Graph each function using a graphing utility and the Change-of-Base Formula.
$y = \log_{x + 2} (x - 2)$

Short Answer

Expert verified

Consider the given function.

$y = \log_{x + 2} (x - 2)$

Step by step solution

01

Step 1. Given information.

Consider the given function.

$y = \log_{x + 2} (x - 2)$

02

Step 2. Calculation.

Apply the change base formula.

$\begin{array}{l} y = \log_{x + 2} (x - 2) \\ = \frac{\log (x - 2)}{\log (x + 2)} \end{array}$

03

Step 3. Graph.

Draw the graph of the obtained base change function.

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Most popular questions from this chapter

In Problems $33 - 40$ , the graph of an exponential function is given. Match each graph to one of the following functions.

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = - e^{x}$

the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{x^{2} - 4}{2 x^{2}} x > 0$

The graph of an exponential function is given. Match each graph to one of the following functions.

Use the graph of $y = f (x)$ given in the Problem $43$ to evaluate the following:

(a) $f (- 1)$

(b) $f (1)$

(c) $f^{- 1} (1)$

(d) $f^{- 1} (2)$

See all solutions

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