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log_(4)256=

log⁡4256= \log _{4} 256=

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Full solution

Q. log⁡4256= \log _{4} 256=
  1. Question prompt: What is the value of log⁡4256\log_{4} 256?
  2. Identify base and number: Identify the base bb and the number xx for the logarithmic equation log⁡(b)(x)\log_{(b)}(x).\newlineIn this case, b=4b = 4 and x=256x = 256.
  3. Recall definition of logarithm: Recall the definition of a logarithm.\newlineThe logarithm log⁡b(x)\log_{b}(x) answers the question: ＂To what power must bb be raised to obtain xx?＂ In other words, if log⁡b(x)=y\log_{b}(x) = y, then by=xb^{y} = x.
  4. Determine power for base 44: Determine the power to which 44 must be raised to get 256256.\newlineWe know that 42=164^2 = 16 and 44=2564^4 = 256. Therefore, 44 must be raised to the power of 44 to get 256256.
  5. Write logarithmic equation: Write the logarithmic equation using the value found in Step 33.\newlineSince 44=2564^4 = 256, we can write the logarithmic equation as log⁡4256=4\log_{4}256 = 4.

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