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log_(8)512=

log⁡8512= \log _{8} 512=

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Full solution

Q. log⁡8512= \log _{8} 512=
  1. Identify base, argument, and unknown exponent: Identify the base (), the argument (), and the unknown exponent () in the logarithmic equation _{(88)}512512 = . In this case,  = 88 and  = 512512. We need to find the value of  such that 88^ = 512512.
  2. Recall logarithms and exponents relationship: Recall the relationship between logarithms and exponents: log⁡bx=y\log_{b}x = y is equivalent to by=xb^{y} = x.\newlineWe need to find the value of yy that makes the equation 8y=5128^{y} = 512 true.
  3. Determine the value of y: Determine the value of y by finding a power of 88 that equals 512512.\newlineWe know that 88^11 = 88, 88^22 = 6464, and 88^33 = 512512.\newlineTherefore, y = 33 because 88^33 = 512512.
  4. Write the equation in exponential form: Write the original logarithmic equation in exponential form using the value of yy found in the previous step.\newlineThe exponential form of log⁡8512\log_{8}512 is 838^3.

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