Identify key elements: Identify the base (b), the argument (x), and the unknown exponent (y) in the logarithmic equation log₂(256) = y. In this case, b = 2, x = 256, and we need to find y such that 2^y = 256.Understand relationship: Recall the relationship between logarithms and exponents: log_b(x) = y is equivalent to b^y = x. We need to find the value of y that makes the equation 2^y = 256 true.Determine value of y: Determine the value of y by finding the power to which 2 must be raised to get 256. We can do this by recognizing that 256 is a power of 2: 2^8 = 256. Therefore, y = 8.Check for errors: Check the calculation for any mathematical errors. 2^8 = 256 is a correct statement, so there are no math errors in the calculation.

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$\log _{2} 256=$

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{2} 256=

Identify key elements: Identify the base $b$ , the argument $x$ , and the unknown exponent $y$ in the logarithmic equation $\log_2(256) = y$ . In this case, $b = 2$ , $x = 256$ , and we need to find $y$ such that $2^y = 256$ .
Understand relationship: Recall the relationship between logarithms and exponents: $\log_b(x) = y$ is equivalent to $b^y = x$ . We need to find the value of $y$ that makes the equation $2^y = 256$ true.
Determine value of $y$ : Determine the value of $y$ by finding the power to which $2$ must be raised to get $256$ . We can do this by recognizing that $256$ is a power of $2$ : $2^8 = 256$ . Therefore, $y = 8$ .
Check for errors: Check the calculation for any mathematical errors. $\newline$ $2^8 = 256$ is a correct statement, so there are no math errors in the calculation.