Identify relationship between base and number: Identify the relationship between the base of the logarithm and the number. The base of the logarithm is 2, and we need to find the power to which 2 must be raised to get 1024.Express number as power of base: Express 1024 as a power of 2. 1024 is a power of 2, and we can find this power by repeatedly dividing 1024 by 2. 1024 = 2^10 because 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1024.Apply definition of logarithm: Apply the definition of a logarithm. Using the definition of a logarithm, log_(2)1024 is the power to which the base 2 must be raised to produce 1024. Since we found that 1024 = 2^10, log_(2)1024 = 10.

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$\log _{2} 1024=$

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Algebra 2

Evaluate logarithms using properties

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\log _{2} 1024=

Identify relationship between base and number: Identify the relationship between the base of the logarithm and the number. $\newline$ The base of the logarithm is $2$ , and we need to find the power to which $2$ must be raised to get $1024$ .
Express number as power of base: Express $1024$ as a power of $2$ . $\newline$ $1024$ is a power of $2$ , and we can find this power by repeatedly dividing $1024$ by $2$ . $\newline$ $1024 = 2^{10}$ because $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024$ .
Apply definition of logarithm: Apply the definition of a logarithm. $\newline$ Using the definition of a logarithm, $\log_{2}1024$ is the power to which the base $2$ must be raised to produce $1024$ . $\newline$ Since we found that $1024 = 2^{10}$ , $\log_{2}1024 = 10$ .