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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 log_b(mn) = log_b(m) + log_b(n), so the log of a product is the sum of the logs.
  • How does the quotient rule for logarithms work?
    The quotient rule states that log_b(m/n) = log_b(m) - log_b(n), so the log of a quotient is the difference of the logs.
  • What is the power rule for logarithms?
    The power rule states that log_b(m^n) = n * log_b(m), so the exponent can be brought in front of the log.
  • How would you expand log base 2 of 3xy^2?
    You expand it as log_2(3) + log_2(x) + 2 * log_2(y) using the product and power rules.
  • When condensing logarithmic expressions, what must you check first?
    You must ensure all logs have the same base before condensing.
  • What is the correct order of applying rules when condensing logs?
    Apply the power rule first, then the quotient rule.
  • How do you change the base of a logarithm from b to a?
    Use the formula log_a(m) = log_b(m) / log_b(a), where the original argument goes on top and the original base on the bottom.
  • Why are common logs (base 10) and natural logs (base e) useful?
    They are useful because calculators have dedicated buttons for them, making calculations easier.
  • What is the result of log base e of e?
    log base e of e equals 1.
  • How would you write log base 5 of 2 using common logs?
    It is written as log(2) / log(5).
  • If you have 2 * ln(x) - ln(x + 2), how do you condense it into a single log?
    First, write it as ln(x^2) - ln(x + 2), then condense to ln(x^2 / (x + 2)).
  • What happens to the answer when you change the base of a log to 10 or e?
    The answer remains the same regardless of whether you use base 10 or base e.
  • How do you expand log base 2 of 3x?
    It expands to log_2(3) + log_2(x) using the product rule.
  • What does multiplication inside a log become when expanded?
    Multiplication inside a log becomes addition of logs when expanded.
  • How do you evaluate log base pi of 9 using natural logs?
    Write it as ln(9) / ln(pi) and evaluate using a calculator.