Algebra Quiz: Logarithmic Expressions And Equations Test

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| By Albert Melchor
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Albert Melchor
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Quizzes Created: 17 | Total Attempts: 12,887
| Attempts: 154
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  • 1/25 Questions
    Find an equivalent for the given equation. - ProProfs

    Find an equivalent for the given equation.

    • Not here
Please wait...
About This Quiz

Ready to tackle the complexities of logarithmic expressions and equations? The Algebra Quiz: Logarithmic Expressions and Equations Test challenges your understanding of key logarithmic concepts, from simplifying expressions to solving equations with precision.

The quiz presents a range of problems that delve into the core properties and rules of logarithms, testing your ability to navigate both basic and advanced levels. This quiz has questions that will deepen your grasp of algebraic principles and strengthen your problem-solving skills. Take the quiz now to find out how well you can master these logarithmic challenges. Are you ready to put your math knowledge to the test?

Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

Quiz Preview

  • 2. 
    Which is the best first step to solving the equation? - ProProfs

    Which is the best first step to solving the equation?

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • None of these

    Correct Answer
    A.
  • 3. 
    Write  in logarithmic form - ProProfs

    Write  in logarithmic form

    Correct Answer
    A.
  • 4. 
    Find an equivalent for the given equation. - ProProfs

    Find an equivalent for the given equation.

    Correct Answer
    A.
  • 5. 
    Find an equivalent for the given equation. - ProProfs

    Find an equivalent for the given equation.

    Correct Answer
    A.
  • 6. 
    Which is the best first step in solving the equation? - ProProfs

    Which is the best first step in solving the equation?

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • None of these

    Correct Answer
    A.
  • 7. 
    Solve the equation. - ProProfs

    Solve the equation.

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Not here

    Correct Answer
    A.  and 
  • 8. 
    Find an equivalent for the given equation. - ProProfs

    Find an equivalent for the given equation.

    Correct Answer
    A.
  • 9. 
    Solve the equation. - ProProfs

    Solve the equation.

    • X = 4

    • X = 16

    • X = 6

    • X = 9

    • Not here

    Correct Answer
    A. 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:

  • 10. 
    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 . - ProProfs

    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 .

    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.

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  • 11. 
    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 . - ProProfs

    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 .

    Correct Answer
    A.
    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:

  • 12. 
    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  - ProProfs

    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 

    • $1287.01

    • $2416.50

    • $2485.49

    • 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.

    Rate this question:

  • 13. 
    Solve the equation. - ProProfs

    Solve the equation.

    • X = 9

    • X = 32

    • X = 16

    • X = 3

    • 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:

  • 14. 
    Which is the best first step in solving the equation? - ProProfs

    Which is the best first step in solving the equation?

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • None of these

    Correct Answer
    A.
  • 15. 
    Express as a single logarithm: - ProProfs

    Express as a single logarithm:

    Correct Answer
    A.
  • 16. 
    Using the properties of logs, write in expanded form: - ProProfs

    Using the properties of logs, write in expanded form:

    Correct Answer
    A.
  • 17. 
    Which is the best first step to solving the equation? - ProProfs

    Which is the best first step to solving the equation?

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • None of these

    Correct Answer
    A.
  • 18. 
    Solve for x. - ProProfs

    Solve for x.

    • 5

    • 10

    • 25

    • 32

    • Not here

    Correct Answer
    A. 25
  • 19. 
    Solve the equation. - ProProfs

    Solve the equation.

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Not here

    Correct Answer
    A.  and 
  • 20. 
    Solve the equation: - ProProfs

    Solve the equation:

    • X = 4

    • X = 3

    • X = 2

    • Not here

    Correct Answer
    A. Not here
  • 21. 
    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,  - ProProfs

    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, 

    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.

    Rate this question:

  • 22. 
    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  - ProProfs

    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 

    • $1051.27

    • $2050.63

    • $1648.72

    • 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.

    Rate this question:

  • 23. 
    Using the properties of logs, write in expanded form: - ProProfs

    Using the properties of logs, write in expanded form:

    Correct Answer
    A.
  • 24. 
    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,  - ProProfs

    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, 

    Correct Answer
    A. Not here
  • 25. 
    Solve the equation. - ProProfs

    Solve the equation.

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    •  and 

      Algebra Quiz: Logarithmic Expressions And Equations Test - Quiz

    • Not here

    Correct Answer
    A.

Quiz Review Timeline (Updated): Sep 1, 2024 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Sep 01, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Dec 04, 2014
    Quiz Created by
    Albert Melchor
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