Define Logarithm: We are asked to find the value of the logarithm of 16 with base 4, which is written as log_(4)16. The logarithm of a number is the exponent to which the base must be raised to produce that number.Identify Base and Number: We know that 4 squared (4^2) equals 16. This means that 4 needs to be raised to the power of 2 to get 16.Calculate Exponent: Therefore, log_(4)16 is asking ＂to what power must 4 be raised to get 16?＂ Since we've established that 4^2 = 16, the answer to this question is 2.Final Answer: So, log_(4)16 = 2. This is the final answer.

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$\log _{4} 16=$

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Grade 8

Relationship between squares and square roots

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\log _{4} 16=

Define Logarithm: We are asked to find the value of the logarithm of $16$ with base $4$ , which is written as $\log_{4}16$ . The logarithm of a number is the exponent to which the base must be raised to produce that number.
Identify Base and Number: We know that $4$ squared ( $4^2$ ) equals $16$ . This means that $4$ needs to be raised to the power of $2$ to get $16$ .
Calculate Exponent: Therefore, $\log_{4}16$ is asking ＂to what power must $4$ be raised to get $16$ ?＂ Since we've established that $4^2 = 16$ , the answer to this question is $2$ .
Final Answer: So, $\log_{4}16 = 2$ . This is the final answer.