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Power and Root Functions quiz #1 Flashcards

Power and Root Functions quiz #1
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  • Which expression is equivalent to the square root of negative 80 (√−80)?
    The square root of negative 80 (√−80) is equivalent to i√80, where i is the imaginary unit (i = √−1).
  • What does log(0.10) equal and why?
    Log(0.10) equals -1 because 0.10 is 10 to the power of -1, and the log function returns the exponent.
  • How does the logarithm function simplify log(10,000)?
    Log(10,000) simplifies to 4 because 10,000 is 10 to the 4th power, and the log function returns the exponent.
  • What is the result of any number raised to the zeroth power, and how does this relate to logarithms?
    Any number raised to the zeroth power equals 1, so log(1) is always 0 because 10 to the 0 is 1.
  • How do you use the antilog to solve for the ratio of conjugate base to weak acid in the Henderson-Hasselbalch equation?
    You take the antilog of the difference between pH and pKa, raising 10 to that value to find the ratio.
  • What does the natural logarithm (ln) of a number represent?
    The natural logarithm of a number is the exponent to which e must be raised to yield that number.
  • How do you find the value of x if ln(x) equals a given number?
    You take the inverse of the natural logarithm by raising e to that number, so x = e^(given number).
  • What happens to the logarithm when you multiply two numbers inside the log function?
    Multiplying two numbers inside the log function results in the sum of their individual logarithms.
  • How is division handled in logarithmic and natural logarithmic functions?
    Division inside the log or ln function translates to the difference of the logarithms: log(a/b) = log(a) - log(b).
  • How do you express the logarithm of an nth root using log properties?
    The logarithm of an nth root, log(a^(1/x)), can be written as (1/x) times log(a).