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log_(4)64=

log⁡464= \log _{4} 64=

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Q. log⁡464= \log _{4} 64=
  1. Identify base, exponent, and result: Identify the base (bb), the exponent (yy), and the result (xx) in the logarithmic equation log⁡464\log_{4}64.\newlineIn a logarithmic equation of the form log⁡bx=y\log_{b}x = y, bb is the base, xx is the result, and yy is the exponent.\newlineHere, b=4b = 4 and x=64x = 64. We need to find yy such that yy11.
  2. Find the value of y: Recall that 6464 is a power of 44. Specifically, 6464 is 44 raised to the power of 33, because 44 \times 44 \times 44 = 6464.\newlineTherefore, y = 33 because 44^33 = 6464.
  3. Write the exponential form: Write the exponential form of the logarithmic equation log⁡464\log_{4}64.\newlineSince we have determined that 43=644^3 = 64, the exponential form of the equation is 43=644^3 = 64.

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