This EduRev document offers 10 Multiple Choice Questions (MCQs) from the topic Exponents & Logarithm (Level - 1). These questions are of Level - 1 difficulty and will assist you in the preparation of CAT & other MBA exams. You can practice/attempt these CAT Multiple Choice Questions (MCQs) and check the explanations for a better understanding of the topic.
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:If log 3 = 0.47712, what will be the number of digits in 3^{64}?
Explanation
log 3 = 0.47712 …. (1)
log (364) = 64 x log 3
= 64 x 0.47712 (from equation1)
= 30.53568
Its characteristic is 30.
Hence, the number of digits in 364 is (30 + 1) = 31
Option (3) is correct.
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:Solve the following equation for x:
log10 x - log10 √x = = 2 log_{x }10
Explanation
log10 x - 1/2 log10 x = 2 logx 10 ...(I)
or, 1/2 log10 x = 2 logx 10 ...(II)
Using base change rule (logb a = 1/loga b), equation (II) becomes:
1/2 log10 x = 2/log10 x
(log10 x)^{2} = 4
or, log10 x = ±2
x = 100 or x = 1/100
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:Find the value of Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:If p^{a} = q^{b} = r^{c} and , then b = Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:If 3^{x} = 4^{y} = 12^{z}, find the value of z.
Explanation
3 = 12^{z/x} ... (1)
4 = 12^{z/y} ... (2)
Multiply (1) and (2);
12 = 12^{(z/x) + (z/y)}
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:The value of log_{4} 3 × log_{5} 4 x … x log_{9} 8 × log_{3} 9 is _______.
Explanation
log_{4} ^{3} × log_{5} ^{4} x … x log_{9} ^{8} × log_{3 }^{9}
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:Find a and b, if Explanation
(Comparing this with a - b √3 : a = 11, b = 6)
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:If the values of log_{10} ^{2}, log_{10 }^{3} and log_{10} ^{7} are known, which one of the following cannot be evaluated?
Explanation
log10 75 = log10 (3 x 5^{2}) = log10 3 + 2log10^{5}
log_{10} ^{252} = log10 (2^{2} x 3^{2} x 7) = 2 log10 ^{2} + 2log10 ^{3} + log10 ^{7}
log_{10} ^{98} = log10 (7^{2} x 2) = 2 log10^{ 7} + log10 ^{2}
All of the above can be easily solved, but log10 770 (log10^{ 7} x log_{10} 11) cannot be solved because log_{10} 11 is unknown.
Hence, option (d) is correct.
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:The possible values of x for the equation log2 x^{2} + logx ^{2} = 3 are
Explanation
log2 x^{2} + logx 2 = 3
⇒ + log_{x} 2 = 3
⇒ 2 + (logx 2)^{2} - 3 log_{x} 2 = 0
Put y = logx 2
⇒ y^{2} - 3y + 2 = 0
⇒ y = 1, 2
For y = 1, logx 2 = 1 or x = 2
For y = 2, logx 2 = 2 or x = √2
Hence, there are two valid values of x, i.e. x = 2, √2.
Question for Practice Questions Level 1: Exponents & Logarithm
Try yourself:A sequence is given by log7 2, log7 4, log7 16, log7 256, ........... The common ratio of this geometric progression is
Explanation
Given sequence can be written as follows.
log7 2, log7 2^{2}, log7 2^{4}, log7 2^{8}, ……….
It can be further written as
log_{7} 2, 2 log_{7} 2, 4 log7 2, 8 log7 2, ………. [log m^{n} = n log m]
By dividing 2nd term by 1st term, we get common ratio, r = = 2