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Properties of Logarithms quiz

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  • What does the product property of logarithms state?
    The product property states that log_b(mn) = log_b(m) + log_b(n), meaning multiplication inside the log becomes addition of logs.
  • How do you expand log base 5 of 3x using log properties?
    You expand it as log base 5 of 3 plus log base 5 of x.
  • When can you condense log_b(m) + log_b(n) into a single logarithm?
    You can condense them if both logs have the same base, resulting in log_b(mn).
  • What is a common mistake students make with log_b(m + n)?
    A common mistake is to think log_b(m + n) equals log_b(m) + log_b(n), but this is incorrect; the property only applies to multiplication, not addition.
  • What does the quotient property of logarithms state?
    The quotient property states that log_b(m/n) = log_b(m) - log_b(n), so division inside the log becomes subtraction of logs.
  • How do you expand log base 10 of 7/x using log properties?
    You expand it as log base 10 of 7 minus log base 10 of x.
  • What must be true about the bases to use the quotient property to condense logs?
    The logs must have the same base to use the quotient property for condensing.
  • Is log_b(m - n) equal to log_b(m) - log_b(n)? Why or why not?
    No, log_b(m - n) is not equal to log_b(m) - log_b(n); the property only applies to division, not subtraction inside the argument.
  • What does the power property of logarithms state?
    The power property states that log_b(m^n) = n * log_b(m), so an exponent inside the log can be moved out front as multiplication.
  • How do you rewrite 4 * log base 5 of x using the power property?
    You rewrite it as log base 5 of x to the 4th power, or log base 5 of x^4.
  • How can you use the power property to expand log base 2 of the square root of 5?
    First, rewrite the square root as a power: log base 2 of 5^(1/2), then expand to (1/2) * log base 2 of 5.
  • What is the first step when condensing a log expression with multiplication out front?
    Apply the power property first by moving the multiplier into the exponent of the argument.
  • How do you fully expand log base 10 of 3xy^2?
    First, use the product property: log base 10 of 3 + log base 10 of x + log base 10 of y^2, then use the power property to get log base 10 of 3 + log base 10 of x + 2*log base 10 of y.
  • When condensing logs, which property should you apply first?
    You should apply the power property first before using the product or quotient properties.
  • Why is it important to rewrite roots and fractions with exponents before using log properties?
    Because the power property applies to exponents, rewriting roots and fractions as exponents allows you to use the property correctly.