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

Read More...

Quantitative Aptitude - Algebra - Logarithms - If x is a real number
Quantitative Aptitude - Algebra - Logarithms
Question
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

Read More...

Quantitative Aptitude - Algebra - Logarithms - If G is the geometric mean
Quantitative Aptitude - Algebra - Logarithms
Question
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

Read More...

Quantitative Aptitude – Algebra - Logarithms – 1/log(base2)100 -1/log(base4)100 +1/log(base5)100
Slot -2 – Quantitative Aptitude – Algebra - Logarithms – 1/log(base2)100 -1/log(base4)100 +1/log(base5)100
1/log(base2)100 -1/log(base4)100 +1/log(base5)100 -1/log(base10)100 +1/log(base20)100 -1/log(base25)100 +1/log(base50)100 ---?
a) ½
b) 10
c) -4
d) 0
Answer: a) ½
Solution:
Using log(basea)b = 1/log(baseb)a
1/log(base2)100 -1/log(base4)100 +1/log(base

Read More...

Quantitative Aptitude – Algebra - Logarithms – If p^3 = q^4 = r^5 = s^6
Slot -2 – Quantitative Aptitude – Algebra - Logarithms – If p^3 = q^4 = r^5 = s^6
If p^3 = q^4 = r^5 = s^6, then the value of log_spqr is equal to?
a) 24/5
b) 16/5
c) 47/10
d) 1
Answer: c) 47/10
Solution:
Let p^3 = q^4 = r^5 = s^6=k
So p=k^(1/3), q=k^(1/4), r=k^(1/5) and s=k^(1/6)
Thus log(base s)pqr = log(base(k^(1/6) )) k^(1/3+1/4+1/5) =6 log(base k) k^((20+15+12)/60)=6×47/60 log(base k) k=47/10
Other p

Read More...

Quantitative Aptitude – Algebra - Logarithms – If x is a positive quantity such that 2^x
Slot -1 – Quantitative Aptitude – Algebra - Logarithms – If x is a positive quantity such that 2^x
If x is a positive quantity such that 2^x = 3^log(base5)^2 , then x is equal to?
a) log(base5)^9
b) 1 + log(base5) 3/5
c) log(base5)^8
d) 1 + log(base3) 5/3
Answer: b) 1 + log(base5) 3/5
Solution:
Given , 2^x = 3^log(base5)2
taking log of both sides ,
x log2 = log(base5) 2 log 3 = (log 2

Read More...

Quantitative Aptitude – Algebra - Logarithms – If log(base12) 81=p then 3
Slot -1 – Quantitative Aptitude – Algebra - Logarithms – If log(base12) 81=p then 3
If log(base12) 81=p then 3 { (4-p)/(4+p)} is equal to
a) log (base2) 8
b) log (base4) 16
c) log (base6) 8
d) log (base6) 16
Solution:
Given , log(base12) 81 = p
4 log (base12) 3 = p
So 3 (4-p)/(4+p) = 3 (1- log(base12) 3 )/(1+ log(base12) 3)=3 × log(base12)(12/3)/log(base12)(12×3) = 3×log(base36) 4 = log(base6)

Read More...

Quantitative Aptitude – Algebra - Logarithms – If log(base2)(5 + log(base3) a)
Slot -1 - Quantitative Aptitude – Algebra - Logarithms – If log(base2)(5 + log(base3) a)
If log2(5 + log3a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to?
a) 59
b) 40
c) 67
d) 32
Solution:
Given, log2(5 + log3 a) = 3
5 + log3 a = 2^3 = 8
log3 a = 3
so a = 3^3 = 27
Now log(base5) (4a+12+log(base2) b)=3
Or 4a + 12 + log(base2) b) = 125
log(base2) b = 125-12-4×27=5
So b = 2^5 = 32
Th

Read More...