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log_(2)64=

$\log _{2} 64=$

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Evaluate logarithms using properties

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Q.

\log _{2} 64=

Question Prompt: Question prompt: What is the value of $\log_{2}64$ ?
Express $64$ as power of $2$ : Recognize that we need to express $64$ as a power of $2$ . $64$ is a power of $2$ because $2$ multiplied by itself $6$ times equals $64$ . $2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$ Therefore, $64 = 2^6$ .
Rewrite using power of $2$ : Rewrite the logarithmic expression using the power of $2$ . $\newline$ $\log_{2}64$ is the same as asking ＂to what power must $2$ be raised to get $64$ ?＂ $\newline$ Since we know that $64 = 2^6$ , we can write: $\newline$ $\log_{2}64 = \log_{2}(2^6)$
Apply power property: Apply the power property of logarithms. The power property of logarithms states that $\log_b(a^c) = c \cdot \log_b(a)$ . In this case, we have $\log_{2}(2^6)$ which simplifies to $6 \cdot \log_{2}(2)$ .
Evaluate expression: Evaluate $6 \times \log_{2}2$ . The logarithm of a number to the same base is $1$ , so $\log_{2}2$ equals $1$ . Therefore, $6 \times \log_{2}2$ equals $6 \times 1$ which is $6$ .

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