Chapter 10: Q. 10.58 (page 1037)

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

Short Answer

Expert verified

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

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

Step by step solution

Step 1. given data

Given logarithm expressions are

ⓐ $2^{\log_{2} (8)}$

ⓑ $\log_{2} 2^{15}$

Step 2. solution of part (a)

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

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

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

Short Answer

Step by step solution

Step 1. given data

Step 2. solution of part (a)

Step 3. solution of part (b)

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