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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 68. (page 309)

Write each expression as a single logarithm.
$\frac{1}{3} \log (x^{3} + 1) + \frac{1}{2} \log (x^{2} + 1)$

Short Answer

Expert verified

The obtained result is $\log [{(x^{3} + 1)}^{\frac{1}{3}} {(x^{2} + 1)}^{\frac{1}{2}}]$ .

Step by step solution

01

Step 1. Given Information.

Consider the given information.

$\frac{1}{3} \log (x^{3} + 1) + \frac{1}{2} \log (x^{2} + 1)$

02

Step 2. Calculation.

Apply the logarithm properties to combine the terms.

$\begin{array}{rcl} \frac{1}{3} \log (x^{3} + 1) + \frac{1}{2} \log (x^{2} + 1) & = & \log {(x^{3} + 1)}^{\frac{1}{3}} + \log {(x^{2} + 1)}^{\frac{1}{2}} \\ = & \log [{(x^{3} + 1)}^{\frac{1}{3}} {(x^{2} + 1)}^{\frac{1}{2}}] \end{array}$

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Most popular questions from this chapter

A function $y = f (x)$ is decreasing on the interval $(0, 5) .$ What conclusions can you draw about the graph of $y = f^{- 1} (x)$ ?

Solve the equation $2^{- x} = 16$

and verify your results using a graphing utility

If $2^{x} = 3$ , what does $4^{- x}$ equal?

Solve the equation ${(\frac{1}{5})}^{x} = \frac{1}{25}$

and verify your results using a graphing utility.

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$f (x) = 1 - 2^{- x / 3}$

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