Question prompt: Question prompt: What is the value of log base 4 of 256?Identify base and number: Identify the base (b) and the number (x) for the logarithmic equation log_(b)(x). In this case, b = 4 and x = 256.Recall definition of logarithm: Recall the definition of a logarithm. The logarithm log_(b)(x) answers the question: ＂To what power must b be raised to obtain x?＂ In other words, if log_(b)(x) = y, then b^y = x.Determine power for base 4: Determine the power to which 4 must be raised to get 256. We know that 4^2 = 16 and 4^4 = 256. Therefore, 4 must be raised to the power of 4 to get 256.Write logarithmic equation: Write the logarithmic equation using the value found in Step 3. Since 4^4 = 256, we can write the logarithmic equation as log_(4)256 = 4.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\log _{4} 256=$

View step-by-step help

Home

Math Problems

Algebra 2

Convert between exponential and logarithmic form: rational bases

Full solution

\log _{4} 256=

Question prompt: What is the value of $\log_{4} 256$ ?
Identify base and number: Identify the base $b$ and the number $x$ for the logarithmic equation $\log_{(b)}(x)$ . $\newline$ In this case, $b = 4$ and $x = 256$ .
Recall definition of logarithm: Recall the definition of a logarithm. $\newline$ The logarithm $\log_{b}(x)$ answers the question: ＂To what power must $b$ be raised to obtain $x$ ?＂ In other words, if $\log_{b}(x) = y$ , then $b^{y} = x$ .
Determine power for base $4$ : Determine the power to which $4$ must be raised to get $256$ . $\newline$ We know that $4^2 = 16$ and $4^4 = 256$ . Therefore, $4$ must be raised to the power of $4$ to get $256$ .
Write logarithmic equation: Write the logarithmic equation using the value found in Step $3$ . $\newline$ Since $4^4 = 256$ , we can write the logarithmic equation as $\log_{4}256 = 4$ .