Properties Of Logs- Review For Quiz
Questions and Answers
- 1.
The equation 2 x = 9 can be entered in the calculator in which form?
- A.
(log 9) / (log 2)
- B.
Log 9 * log 2
- C.
(log 9 )^2
- D.
(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).Rate this question:
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- 2.
A logarithmic function is the inverse of which function?
- A.
Quadratic
- B.
Linear
- C.
Cubic
- D.
Exponential
Correct Answer
D. 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
- A.
2
- B.
3
- C.
4
- D.
8
Correct Answer
B. 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
- A.
3 + log2m + log2n
- B.
3 + log2m - log2n
- C.
Log28 + log2mn
- D.
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
- A.
Log (m3n2p)
- B.
Log(m/(n2p)0.5
- C.
Log (m3/(n2p0.5)
- D.
Log(1/(m3n2p)
Correct Answer
C. 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)
- A.
True
- B.
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
- A.
Log( cube root of m, times, n)
- B.
Log (square root of m, times, the cube root of n)
- C.
Log( 6th root of mn)
- D.
Log (square roots of m, divided by, the cube root of n)
Correct Answer
B. 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
- A.
F(x)=log2x
- B.
F(x)=log2(x-1)
- C.
F(x)=2x
- D.
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
- A.
2.718
- B.
0.367
- C.
0
- D.
2.727
Correct Answer
D. 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
ProProfs Editorial Team -
Jan 30, 2017Quiz Created by
Jerbe
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