Question

Evaluate using the properties of logarithms: ⓐ$2^{{\log }_2\left(8\right)}$ ⓑ${\log }_2{2}^{15}$

Short answer

ⓐ value of the $2^{{\log }_2\left(8\right)}$is$8$

ⓑ value of the ${\log }_2{2}^{15}$is$15$

Step-by-step solution

Step 1. given data

Given logarithm expressions are

ⓐ$2^{{\log }_2\left(8\right)}$

ⓑ${\log }_2{2}^{15}$

Step 2. solution of part (a)

Use Inverse Properties of Logarithms$a^{{\log }_a\left(x\right)}=x$

so$2^{{\log }_2\left(8\right)}=8$

Step 3. solution of part (b)

Use Inverse Properties of Logarithms${\log }_a\left(a^x\right)=x$

so${\log }_2{2}^{15}=15$