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 * 2 * 2 * 2 * 2 * 2 = 64 Therefore, 64 = 2^6.Rewrite using power of 2: Rewrite the logarithmic expression using the power of 2. log_(2)64 is the same as asking ＂to what power must 2 be raised to get 64?＂ Since we know that 64 = 2^6, we can write: 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 * log_b(a). In this case, we have log_(2)(2^6) which simplifies to 6 * log_(2)2.Evaluate expression: Evaluate 6 * log_(2)2. The logarithm of a number to the same base is 1, so log_(2)2 equals 1. Therefore, 6 * log_(2)2 equals 6 * 1 which is 6.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\log _{2} 64=$

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate logarithms using properties

Full solution

\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 $6$ .