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log_(4)16=

$\log _{4} 16=$

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Relationship between squares and square roots

Full solution

Q.

\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.

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