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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 10.58 (page 1037)

Evaluate using the properties of logarithms: 鈸� $2^{\log_{2} (8)}$ 鈸� $\log_{2} 2^{15}$

Short Answer

Expert verified

鈸� value of the $2^{\log_{2} (8)}$ is $8$

鈸� value of the $\log_{2} 2^{15}$ is $15$

Step by step solution

01

Step 1. given data

Given logarithm expressions are

鈸� $2^{\log_{2} (8)}$

鈸� $\log_{2} 2^{15}$

02

Step 2. solution of part (a)

Use Inverse Properties of Logarithms $a^{\log_{a} (x)} = x$

so $2^{\log_{2} (8)} = 8$

03

Step 3. solution of part (b)

Use Inverse Properties of Logarithms $\log_{a} (a^{x}) = x$

so $\log_{2} 2^{15} = 15$

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Most popular questions from this chapter

In the following exercises, graph each function in the same coordinate system:

$f (x) = 3^{x}, g (x) = 3^{x} + 2$

In the following exercises, match the graphs to one of the following functions:

$鈸� 2^{x} 鈸� 2^{x + 1} 鈸� 2^{x - 1} 鈸� 2^{x} + 2 鈸� 2^{x} 鈭� 2 鈸� 3^{x}$

Find the inverse of the function , $f (x) = \sqrt[5]{3 x - 2}$

Find the inverse of the function , $f (x) = \sqrt[4]{6 x - 7}$

On the same coordinate system, graph:

$f (x) = 3^{x}$

$g (x) = 3^{x} + 2$

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