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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 26. (page 308)

Use properties of logarithms to find the exact value of each expression. Do not use a calculator.
$5^{\log_{5} 6 + \log_{5} 7}$

Short Answer

Expert verified

The value is 42.

Step by step solution

01

Step 1. Given information.

Consider the given information.

$5^{\log_{5} 6 + \log_{5} 7}$

02

Step 2. Logarithm properties.

The properties are defined as,

$\begin{array}{l} a^{\log_{a} (b)} = b \\ \log (M N) = \log_{a} M + \log_{a} N \end{array}$

03

Step 3. Calculation.

Apply the properties.

$\begin{array}{l} 5^{\log_{5} 6 + \log_{5} 7} = 5^{\log_{5} (6 路 7)} \\ = 5^{\log_{5} (42)} \\ = 42 \end{array}$

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Most popular questions from this chapter

Do you think that there is a power function that increases

more rapidly than an exponential function whose base is greater than 1 ? Explain.

Solve the equation $5^{x + 3} = \frac{1}{5}$

and verify your results using a graphing utility.

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

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

If $f (x) = a^{x}$ , show that $f (- x) = \frac{1}{f (x)}$ .

If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f 鈭� g$ crosses the y-axis at 23.

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