Properties Of Logs- Review For Quiz
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The equation 2 x = 9 can be entered in the calculator in which form?
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(log 9) / (log 2)
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Log 9 * log 2
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(log 9 )^2
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(log 2) / (log 9)
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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.
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- 2.
A logarithmic function is the inverse of which function?
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Quadratic
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Linear
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Cubic
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Exponential
Correct Answer
A. ExponentialExplanation
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.Rate this question:
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- 3.
Condense using log properties, then simplify
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2
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3
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4
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8
Correct Answer
A. 3Explanation
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.Rate this question:
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- 4.
Expand: log28mn
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3 + log2m + log2n
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3 + log2m - log2n
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Log28 + log2mn
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2 + log28 - log2mn
Correct Answer
A. 3 + log2m + log2nExplanation
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.Rate this question:
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- 5.
Write as a single logarithm: 3logm - 2logn - 0.5logp
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Log (m3n2p)
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Log(m/(n2p)0.5
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Log (m3/(n2p0.5)
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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)).Rate this question:
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- 6.
The following expression: 3 - log3n is the correct expansion of : log3(27/n)
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True
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False
Correct Answer
A. TrueExplanation
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.Rate this question:
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- 7.
Logarithmic functions always have ________ asymptotes?
Correct Answer
VerticalExplanation
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.Rate this question:
- 8.
Describe the following expression as a single logarithm: (1/2)logm + (1/3) logn
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Log( cube root of m, times, n)
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Log (square root of m, times, the cube root of n)
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Log( 6th root of mn)
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Log (square roots of m, divided by, the cube root of n)
Correct Answer
A. Log (square root of m, times, the cube root of n)Explanation
The given expression (1/2)logm + (1/3)logn can be simplified by using the property of logarithms that states loga + logb = log(ab). Applying this property, we can rewrite the expression as log(sqrt(m)) + log(cbrt(n)). Since the logarithm of a product is equal to the sum of the logarithms of its factors, this can be further simplified to log(sqrt(m) * cbrt(n)). Therefore, the correct answer is "log (square root of m, times, the cube root of n)".Rate this question:
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- 9.
What is the parent function of : f(x)=log2(x-1)+3
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F(x)=log2x
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F(x)=log2(x-1)
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F(x)=2x
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F(x)=ln(2)
Correct Answer
A. F(x)=log2xExplanation
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.Rate this question:
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- 10.
Use the Change of Base formula to evaluate the following: log320
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2.718
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0.367
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0
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2.727
Correct Answer
A. 2.727Explanation
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.Rate this question:
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Current Version
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Mar 14, 2023Quiz Edited by
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Jan 30, 2017Quiz Created by
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