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

log (square root of m, times, the cube root of n)

log (square roots of m, divided by, the cube root of n)

Properties Of Logs- Review For Quiz

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| By Jerbe

Jerbe

Community Contributor

Quizzes Created: 1 | Total Attempts: 121

Questions: 10 | Attempts: 121 | Updated: Mar 14, 2023

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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).

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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. 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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3.

Condense using log properties, then simplify
- A.
  
  2
- B.
  
  3
- C.
  
  4
- D.
  
  8
Correct Answer
B. 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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4.

Expand: log₂8mn
- A.
  
  3 + log₂m + log₂n
- B.
  
  3 + log₂m - log₂n
- C.
  
  Log₂8 + log₂mn
- D.
  
  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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5.

Write as a single logarithm: 3logm - 2logn - 0.5logp
- A.
  
  Log (m³n²p)
- B.
  
  Log(m/(n²p)^0.5
- C.
  
  Log (m³/(n²p^0.5)
- D.
  
  Log(1/(m³n²p)
Correct Answer
C. Log (m³/(n²p^0.5)

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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6.

The following expression: 3 - log₃n is the correct expansion of : log₃(27/n)
- A.
  
  True
- B.
  
  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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7.

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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4
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)".

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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)=2^x
- D.
  
  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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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. 2.727

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

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Jan 30, 2017

Quiz Created by
Jerbe

Properties Of Logs- Review For Quiz

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

A logarithmic function is the inverse of which function?

Condense using log properties, then simplify

Expand: log28mn

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

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

Logarithmic functions always have ________ asymptotes?

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

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

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

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

Expand: log₂8mn

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

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

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