Quantitative Aptitude – Algebra – Logarithms – If log (2^a × 3^b × 5^c)

Quantitative Aptitude – Algebra – Logarithms

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Logarithms - If log (2^a × 3^b × 5^c)
If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2^2 × 3^3 × 5), log (2^6 × 3 × 5^7), and log(2 × 3^2 × 5^4), then a equals

Answer

3

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Logarithms, we can see that,
log (2^a. 3^b. 5^c) = [log (2^2.3^3.5) + log (2^6.3.5^7) + log (2.3^2.5^4)]/3
3 * log (2^a. 3^b. 5^c) = log (2^9.3^6.5^12)
log (2^a. 3^b. 5^c)^3 = log (2^9.3^6.5^12)
log (2^3a. 3^3b. 5^3c) = log (2^9.3^6.5^12)
3a = 9
a=3
Answer: 3

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

Logarithm Concepts Questions and Answers for CAT 2018 Quant Preparation

Q1: If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?
Check answer of logarithm Q1

Q2: The value of log (base 0.008) √5 + log (base√3) 81 – 7 is equal to
Check answer of logarithm Q2

Q3: Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to
Check answer of logarithm Q3

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Quantitative Aptitude – Algebra – Logarithms – If log (2^a × 3^b × 5^c)
5 (100%) 55 votes

Quantitative Aptitude – Algebra – Logarithms – If x is a real number

Quantitative Aptitude – Algebra – Logarithms

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Logarithms - If x is a real number
If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?

A) 0 < x < 3
B) 23 < x < 30
C) x > 30
D) 3 < x < 23

Answer

Option (D)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Logarithms, we can see that,
Log(base 3)5 lies between 1 and 2 because Log(base 3)3 = 1 and Log(base 3)9 = 2
1 < Log(base 3)5 < 2
So, log(base 5)(2+x) should also lie between 1 and 2
1 < log(base 5)(2+x) < 2
5^1 < 2+x < 5^2
5 < 2+x < 25
3 < x < 23
Option D is the right answer.

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

Logarithm Concepts Questions and Answers for CAT 2018 Quant Preparation

Q1: If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2^2 × 3^3 × 5), log (2^6 × 3 × 5^7), and log(2 × 3^2 × 5^4), then a equals
Check answer of logarithm Q1

Q2: The value of log (base 0.008) √5 + log (base√3) 81 – 7 is equal to
Check answer of logarithm Q2 

Q3: Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to
Check answer of logarithm Q3

Other posts related to Quantitative Aptitude – Algebra

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How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Know More about Online CAT Course

Quantitative Aptitude – Algebra – Logarithms – If x is a real number
5 (100%) 53 votes

Quantitative Aptitude – Algebra – Logarithms – The value of log(base 0.008)√5

Quantitative Aptitude – Algebra – Logarithms

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Logarithms - The value of log(base 0.008)√5
The value of log (base 0.008) √5 + log (base√3) 81 – 7 is equal to

A) 1/3
B) 2/3
C) 5/6
D) 7/6

Answer

Option (C)

Solution

As per CAT 2017 – Quantitative Aptitude – Algebra – Logarithms, we can see that
log(base 0.008)5^(1/2) = -1/6
Log (base 3^1/2) 3^4 = 8
So, -1/6 + 8 – 7 = 5/6
Option (C)

Logarithm Concepts Questions and Answers for CAT 2018 Quant Preparation

Q1: If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2^2 × 3^3 × 5), log (2^6 × 3 × 5^7), and log(2 × 3^2 × 5^4), then a equals
Check answer of logarithm Q1

Q2: If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?
Check answer of logarithm Q2

Q3: Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to
Check answer of logarithm Q3

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

Other posts related to Quantitative Aptitude – Algebra

Problems on Ages with complete solutions, answers, and tricks to solve
How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Know More about Online CAT Course

Quantitative Aptitude – Algebra – Logarithms – The value of log(base 0.008)√5
5 (100%) 54 votes

Quantitative Aptitude – Algebra – Logarithms – If G is the geometric mean

Quantitative Aptitude – Algebra – Logarithms

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Logarithms - If G is the geometric mean
Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to

A) √a
B) 2a
C) a/2
D) a

Answer

Option (D)

Solution

As per CAT 2017 – Quantitative Aptitude – Algebra – Logarithms, we can see that
x=3^a and y=12^a
G = √(3^a * 12^a) = 6^a
Log (base 6) 6^a = a
Option (D)

Logarithm Concepts Questions and Answers for CAT 2018 Quant Preparation

Q1: If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2^2 × 3^3 × 5), log (2^6 × 3 × 5^7), and log(2 × 3^2 × 5^4), then a equals
Check answer of logarithm Q1

Q2: If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?
Check answer of logarithm Q2

Q3: The value of log (base 0.008) √5 + log (base√3) 81 – 7 is equal to
Check answer of logarithm Q3

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

Other posts related to Quantitative Aptitude – Algebra

Problems on Ages with complete solutions, answers, and tricks to solve
How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Know More about Online CAT Course

Quantitative Aptitude – Algebra – Logarithms – If G is the geometric mean
5 (100%) 55 votes