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Properties of Logarithms quiz

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  • What does the product rule for logarithms state?
    The product rule states that the log of a product is the sum of the logs: log_b(mn) = log_b(m) + log_b(n).
  • How does the quotient rule for logarithms work?
    The quotient rule states that the log of a quotient is the difference of the logs: log_b(m/n) = log_b(m) - log_b(n).
  • What does the power rule for logarithms allow you to do?
    The power rule allows you to bring an exponent in front of the log: log_b(m^n) = n * log_b(m).
  • When expanding log base 2 of 3x, what is the result?
    It expands to log base 2 of 3 plus log base 2 of x.
  • How do you expand log base 2 of 3xy^2 fully?
    It expands to log base 2 of 3 plus log base 2 of x plus 2 times log base 2 of y.
  • What must be true about the bases when condensing logarithms?
    All logs must have the same base before condensing them into a single log.
  • What is the first rule you should apply when condensing logs?
    Apply the power rule first before using the product or quotient rules.
  • How do you condense 2 ln(x) - ln(x + 2)?
    It condenses to ln(x^2 / (x + 2)).
  • How can you change the base of log_b(m) to base a?
    Use the formula log_b(m) = log_a(m) / log_a(b).
  • What is the common log and what base does it use?
    The common log is log base 10 and is written simply as log.
  • What is the natural log and what base does it use?
    The natural log is log base e and is written as ln.
  • How do you evaluate log base 7 of 31 using common logs?
    Write it as log(31) / log(7) and evaluate using a calculator.
  • Does changing the base of a logarithm affect its value?
    No, changing the base using the change of base formula does not affect the final value.
  • How do you simplify ln(e)?
    ln(e) simplifies to 1 because the natural log of e is 1.
  • What is the result of condensing log base 5 of 5 minus log base 5 of y?
    It condenses to log base 5 of (5/y).