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log_(2)16

$1$ ) $\log _{2} 16$

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Product property of logarithms

Full solution

Q.

1

)

\log _{2} 16

Identify Relationship: Identify the relationship between the base of the logarithm and the number inside the logarithm. $\newline$ We are given $\log_{2} 16$ , and we know that $16$ is a power of $2$ . Specifically, $16$ is $2$ raised to the power of $4$ , since $2^4 = 16$ .
Apply Definition: Apply the definition of a logarithm. $\newline$ The logarithm $\log_{2} 16$ asks for the power to which $2$ must be raised to get $16$ . Since we know from Step $1$ that $2^{4} = 16$ , the answer to $\log_{2} 16$ is $4$ .

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