Properties Of Logs- Review For Quiz

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Quizzes Created: 1 | Total Attempts: 137
| Attempts: 137
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  • 1/10 Questions

    Describe the following expression as a single logarithm: (1/2)logm + (1/3) logn

    • Log( cube root of m, times, n)
    • Log (square root of m, times, the cube root of n)
    • Log( 6th root of mn)
    • Log (square roots of m, divided by, the cube root of n)
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About This Quiz

This 'Properties of Logs- Review for Quiz' assesses understanding of logarithmic properties and functions. It includes expanding logarithms, converting expressions into single logarithms, and identifying properties of logarithmic functions, essential for students mastering advanced mathematical concepts.

Properties Of Logs- Review For Quiz - Quiz

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  • 2. 

    Write as a single logarithm: 3logm - 2logn - 0.5logp

    • Log (m3n2p)

    • Log(m/(n2p)0.5

    • Log (m3/(n2p0.5)

    • Log(1/(m3n2p)

    Correct Answer
    A. Log (m3/(n2p0.5)
    Explanation
    The given expression can be simplified by using the properties of logarithms. By applying the power rule of logarithms, we can rewrite the expression as log(m^3) - log(n^2) - log(p^0.5). Then, using the quotient rule of logarithms, we can combine the terms to get log(m^3/(n^2*p^0.5)). Therefore, the correct answer is log(m^3/(n^2*p^0.5)).

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  • 3. 

    A logarithmic function is the inverse of which function?

    • Quadratic

    • Linear

    • Cubic

    • Exponential

    Correct Answer
    A. Exponential
    Explanation
    A logarithmic function is the inverse of an exponential function. This means that if we have an exponential function y = a^x, the logarithmic function that undoes this operation is y = log base a of x. The logarithmic function "undoes" the exponential function by finding the power to which the base must be raised to obtain a certain value. Therefore, the correct answer is exponential.

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  • 4. 

    Logarithmic functions always have ________ asymptotes?

    Correct Answer
    Vertical
    Explanation
    Logarithmic functions always have vertical asymptotes. This is because the domain of a logarithmic function is restricted to positive real numbers. As the input approaches zero, the output of the logarithmic function approaches negative infinity. Therefore, the graph of a logarithmic function approaches a vertical line, which is the vertical asymptote, as the input approaches zero.

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  • 5. 

    What is the parent function of : f(x)=log2(x-1)+3

    • F(x)=log2x

    • F(x)=log2(x-1)

    • F(x)=2x

    • F(x)=ln(2)

    Correct Answer
    A. F(x)=log2x
    Explanation
    The correct answer is f(x)=log2x. This is because the given function f(x)=log2(x-1)+3 is a transformation of the parent function f(x)=log2x. The +3 in the given function represents a vertical shift upwards by 3 units, but the base function remains the same. Therefore, the parent function is f(x)=log2x.

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  • 6. 

    The equation 2 x = 9 can be entered in the calculator in which form?

    • (log 9) / (log 2)

    • Log 9 * log 2

    • (log 9 )^2

    • (log 2) / (log 9)

    Correct Answer
    A. (log 9) / (log 2)
    Explanation
    To solve the equation 2x = 9, we need to isolate x. One way to do this is by using logarithms. Taking the logarithm of both sides of the equation, we get log(2x) = log(9). By the logarithmic property, we can bring down the exponent, so x * log(2) = log(9). To isolate x, we divide both sides of the equation by log(2), giving us x = log(9) / log(2). Therefore, the correct form to enter the equation 2x = 9 into the calculator is (log 9) / (log 2).

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  • 7. 

    The following expression: 3 - log3n is the correct expansion of : log3(27/n)

    • True

    • False

    Correct Answer
    A. True
    Explanation
    The expression 3 - log3n is the correct expansion of log3(27/n) because when we apply the logarithmic property loga(b/c) = loga(b) - loga(c), we can rewrite log3(27/n) as log3(27) - log3(n), which simplifies to 3 - log3n.

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  • 8. 
    Condense using log properties, then simplify  - ProProfs

    Condense using log properties, then simplify 

    • 2

    • 3

    • 4

    • 8

    Correct Answer
    A. 3
    Explanation
    The given expression can be simplified by using the property of logarithms that states log(a) + log(b) = log(a * b). By applying this property, we can condense the expression into log(2 * 3 * 4 * 8). Further simplification gives us log(192), which is equal to 3.

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  • 9. 

    Expand: log28mn

    • 3 + log2m + log2n

    • 3 + log2m - log2n

    • Log28 + log2mn

    • 2 + log28 - log2mn

    Correct Answer
    A. 3 + log2m + log2n
    Explanation
    The given expression is log28mn. Using the logarithmic property log(ab) = log(a) + log(b), we can rewrite the expression as log28 + log2m + log2n. Therefore, the correct answer is 3 + log2m + log2n.

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  • 10. 

    Use the Change of Base formula to evaluate the following: log320

    • 2.718

    • 0.367

    • 0

    • 2.727

    Correct Answer
    A. 2.727
    Explanation
    The correct answer is 2.727. To evaluate log320, we can use the change of base formula which states that log base a of b can be calculated as log base c of b divided by log base c of a. In this case, we can use the natural logarithm (log base e) as the base c. So, log320 can be calculated as log base e of 20 divided by log base e of 3. Evaluating this expression gives us approximately 2.727.

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  • Current Version
  • Mar 14, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jan 30, 2017
    Quiz Created by
    Jerbe
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