What is the value of log_(2)4 ? Answer:

Understand Logarithm Concept: Recognize that the logarithm log₂(4) asks for the power to which the base 2 must be raised to obtain the number 4. Since 2 squared (2²) equals 4, we can write this as log₂(2²).Apply Power Rule: Apply the power rule of logarithms, which states that log_b(a^c) = c * log_b(a), where b is the base, a is the argument, and c is the exponent. In this case, we have log₂(2²) which simplifies to 2 * log₂(2).Evaluate log₂(2): Evaluate log₂(2). Since the base and the argument are the same, the logarithm equals 1. Therefore, 2 * log₂(2) simplifies to 2 * 1.Perform Multiplication: Perform the multiplication to find the final value. 2 * 1 equals 2.

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What is the value of $\log _{2} 4$ ? $\newline$ Answer:

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Precalculus

Product property of logarithms

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Q. What is the value of

\log _{2} 4

\newline

Answer:

Understand Logarithm Concept: Recognize that the logarithm $\log_2(4)$ asks for the power to which the base $2$ must be raised to obtain the number $4$ . Since $2$ squared ( $2^2$ ) equals $4$ , we can write this as $\log_2(2^2)$ .
Apply Power Rule: Apply the power rule of logarithms, which states that $\log_b(a^c) = c \cdot \log_b(a)$ , where $b$ is the base, $a$ is the argument, and $c$ is the exponent. $\newline$ In this case, we have $\log_2(2^2)$ which simplifies to $2 \cdot \log_2(2)$ .
Evaluate $\log_2(2)$ : Evaluate $\log_2(2)$ . Since the base and the argument are the same, the logarithm equals $1$ . Therefore, $2 \times \log_2(2)$ simplifies to $2 \times 1$ .
Perform Multiplication: Perform the multiplication to find the final value. $2 \times 1$ equals $2$ .