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log_(2)256=

log⁡2256= \log _{2} 256=

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Full solution

Q. log⁡2256= \log _{2} 256=
  1. Identify key elements: Identify the base bb, the argument xx, and the unknown exponent yy in the logarithmic equation log⁡2(256)=y\log_2(256) = y. In this case, b=2b = 2, x=256x = 256, and we need to find yy such that 2y=2562^y = 256.
  2. Understand relationship: Recall the relationship between logarithms and exponents: log⁡b(x)=y\log_b(x) = y is equivalent to by=xb^y = x. We need to find the value of yy that makes the equation 2y=2562^y = 256 true.
  3. Determine value of yy: Determine the value of yy by finding the power to which 22 must be raised to get 256256. We can do this by recognizing that 256256 is a power of 22: 28=2562^8 = 256. Therefore, y=8y = 8.
  4. Check for errors: Check the calculation for any mathematical errors.\newline28=2562^8 = 256 is a correct statement, so there are no math errors in the calculation.

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