4-5 And 4-6 Quiz: Logarithmic Expressions And Equations

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| By Albert Melchor
A
Albert Melchor
Community Contributor
Quizzes Created: 17 | Total Attempts: 12,609
Questions: 25 | Attempts: 116

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4-5 And 4-6 Quiz: Logarithmic Expressions And Equations - Quiz

Questions and Answers
  • 1. 

    Write  in logarithmic form

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    C.
  • 2. 

    Solve for x.

    • A.

      5

    • B.

      10

    • C.

      25

    • D.

      32

    • E.

      Not here

    Correct Answer
    C. 25
  • 3. 

    Solve the equation.

    • A.

      X = 9

    • B.

      X = 32

    • C.

      X = 16

    • D.

      X = 3

    • E.

      Not here

    Correct Answer
    A. X = 9
    Explanation
    The given equation is x = 9. This means that the value of x is equal to 9.

    Rate this question:

  • 4. 

    Solve the equation.

    • A.

      X = 4

    • B.

      X = 16

    • C.

      X = 6

    • D.

      X = 9

    • E.

      Not here

    Correct Answer
    C. X = 6
    Explanation
    The given equation has multiple values of x. However, the correct answer is x = 6 because it is the only value that is listed in the options provided. The other values (4, 16, and 9) are not listed as possible solutions, so they are not the correct answers.

    Rate this question:

  • 5. 

    Solve the equation.

    • A.

       and 

    • B.

       and 

    • C.

       and 

    • D.

       and 

    • E.

      Not here

    Correct Answer
    B.  and 
  • 6. 

    Solve the equation.

    • A.

       and 

    • B.

       and 

    • C.
    • D.

       and 

    • E.

      Not here

    Correct Answer
    A.  and 
  • 7. 

    Solve the equation.

    • A.

       and 

    • B.
    • C.
    • D.

       and 

    • E.

      Not here

    Correct Answer
    C.
  • 8. 

    Find an equivalent for the given equation.

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    A.
  • 9. 

    Find an equivalent for the given equation.

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    A.
  • 10. 

    Find an equivalent for the given equation.

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    B.
  • 11. 

    Find an equivalent for the given equation.

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    A.
  • 12. 

    Which is the best first step to solving the equation?

    • A.
    • B.
    • C.
    • D.

      None of these

    Correct Answer
    A.
  • 13. 

    Which is the best first step to solving the equation?

    • A.
    • B.
    • C.
    • D.

      None of these

    Correct Answer
    A.
  • 14. 

    Which is the best first step in solving the equation?

    • A.
    • B.
    • C.
    • D.

      None of these

    Correct Answer
    A.
  • 15. 

    Which is the best first step in solving the equation?

    • A.
    • B.
    • C.
    • D.

      None of these

    Correct Answer
    A.
  • 16. 

    The number of bacteria of a certain type can increase from 80 to 164 in 3 hours.  Find the value of k in the general formula for growth and decay, 

    • A.
    • B.
    • C.
    • D.
    • E.

      Not here

    Correct Answer
    A.
    Explanation
    The general formula for growth and decay is given by the equation: N(t) = N0 * e^(kt), where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is the base of the natural logarithm, and k is the growth or decay constant. In this case, we know that the initial number of bacteria is 80 and the number of bacteria after 3 hours is 164. Plugging these values into the formula, we can solve for k.

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  • 17. 

    Jason invests $1000 in an account that pays 2.5% interest compounded continuously.  To the nearest cent, how much will be in the account at the end of 2 years?  Use 

    • A.

      $1051.27

    • B.

      $2050.63

    • C.

      $1648.72

    • D.

      Not here

    Correct Answer
    A. $1051.27
    Explanation
    Jason invests $1000 in an account that pays 2.5% interest compounded continuously. Continuous compounding means that the interest is constantly being added to the account balance. To calculate the amount in the account at the end of 2 years, we can use the formula A = P * e^(rt), where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm, r is the interest rate, and t is the time in years. Plugging in the values, we get A = 1000 * e^(0.025 * 2) ≈ $1051.27.

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  • 18. 

    The Allen Electric Company has a piece of machinery valued at $60,000.  It depreciates at 20% per year.  After how many years will the value have depreciated to $15,000?  Use .

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    A.
    Explanation
    The value of the machinery depreciates at a rate of 20% per year. To find out how many years it will take for the value to depreciate to $15,000, we need to calculate the depreciation amount per year. The depreciation amount per year can be found by multiplying the initial value of the machinery ($60,000) by the depreciation rate (20% or 0.2). The depreciation amount per year is $12,000. To find out how many years it will take for the value to depreciate to $15,000, we divide the difference between the initial value and the desired value ($60,000 - $15,000 = $45,000) by the depreciation amount per year ($12,000). Therefore, it will take approximately 3.75 years for the value to depreciate to $15,000.

    Rate this question:

  • 19. 

    The number of bacteria of a certain type can increase from 30 to 254 in 3 hours.  Find the value of k in the general formula for growth and decay, 

    • A.
    • B.
    • C.
    • D.
    • E.

      Not here

    Correct Answer
    E. Not here
  • 20. 

    Jason invests $1200 in an account that pays 3.5% interest compounded continuously.  To the nearest cent, how much will be in the account at the end of 2 years?  Use 

    • A.

      $1287.01

    • B.

      $2416.50

    • C.

      $2485.49

    • D.

      Not here

    Correct Answer
    A. $1287.01
    Explanation
    The formula for calculating the amount in an account with continuous compounding is A = P * e^(rt), where A is the final amount, P is the principal amount, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years. Plugging in the values, we get A = 1200 * e^(0.035 * 2) = 1200 * e^(0.07) ≈ $1287.01. Therefore, the correct answer is $1287.01.

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  • 21. 

    The Allen Electric Company has a piece of machinery valued at $45,000.  It depreciates at 20% per year.  After how many years will the value have depreciated to $15,000?  Use .

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    B.
    Explanation
    The value of the machinery decreases by 20% each year. To find out how many years it takes for the value to depreciate to $15,000, we can set up an equation. Let x represent the number of years. The equation would be: $45,000 * (1 - 0.20)^x = $15,000. By solving this equation, we can find the value of x, which represents the number of years it takes for the machinery to depreciate to $15,000.

    Rate this question:

  • 22. 

    Using the properties of logs, write in expanded form:

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    C.
  • 23. 

    Using the properties of logs, write in expanded form:

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    C.
  • 24. 

    Express as a single logarithm:

    • A.
    • B.
    • C.
    • D.

      Not here

    Correct Answer
    A.
  • 25. 

    Solve the equation:

    • A.

      X = 4

    • B.

      X = 3

    • C.

      X = 2

    • D.

      Not here

    Correct Answer
    D. Not here

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Dec 04, 2014
    Quiz Created by
    Albert Melchor
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