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Test Level 1: Exponents and Logarithm - CAT MCQ


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10 Questions MCQ Test Level-wise Tests for CAT - Test Level 1: Exponents and Logarithm

Test Level 1: Exponents and Logarithm for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 1: Exponents and Logarithm questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Exponents and Logarithm MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Exponents and Logarithm below.
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Test Level 1: Exponents and Logarithm - Question 1

If log 3 = 0.47712, what will be the number of digits in 364?

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 1

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.

Test Level 1: Exponents and Logarithm - Question 2

Solve the following equation for x:
log10 x - log10 √x = = 2 logx 10

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 2

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

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Test Level 1: Exponents and Logarithm - Question 3

Find the value of 

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 3

Test Level 1: Exponents and Logarithm - Question 4

If pa = qb = rc and , then b =

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 4

pa = qb = rc = k (Assume)

Given: 
⇒ q2 = pr

Test Level 1: Exponents and Logarithm - Question 5

If 3x = 4y = 12z, find the value of z.

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 5

3 = 12z/x ... (1)
4 = 12z/y ... (2)
Multiply (1) and (2);
12 = 12(z/x) + (z/y)

Test Level 1: Exponents and Logarithm - Question 6

The value of log4 3 × log5 4 x … x log9 8 × log3 9 is _______.

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 6

log4 3 × log5 4 x … x log9 8 × log3 9

Test Level 1: Exponents and Logarithm - Question 7

Find a and b, if

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 7


(Comparing this with a - b √3 : a = 11, b = 6)

Test Level 1: Exponents and Logarithm - Question 8

If the values of log10 2, log10 3 and log10 7 are known, which one of the following cannot be evaluated?

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 8

log10 75 = log10 (3 x 52) = log10 3 + 2log105
log10 252 = log10 (22 x 32 x 7) = 2 log10 2 + 2log10 3 + log10 7
log10 98 = log10 (72 x 2) = 2 log10 7 + log10 2
All of the above can be easily solved, but log10 770 (log10 7 x log10 11) cannot be solved because log10 11 is unknown.
Hence, option (d) is correct.

Test Level 1: Exponents and Logarithm - Question 9

The possible values of x for the equation log2 x2 + logx 2 = 3 are

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 9

log2 x2 + logx 2 = 3
⇒ + logx 2 = 3
⇒ 2 + (logx 2)2 - 3 logx 2 = 0
Put y = logx 2
⇒ y2 - 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.

Test Level 1: Exponents and Logarithm - Question 10

A sequence is given by log7 2, log7 4, log7 16, log7 256, ........... The common ratio of this geometric progression is

Detailed Solution for Test Level 1: Exponents and Logarithm - Question 10

Given sequence can be written as follows.
log7 2, log7 22, log7 24, log7 28, ……….
It can be further written as
log7 2, 2 log7 2, 4 log7 2, 8 log7 2, ………. [log mn = n log m]
By dividing 2nd term by 1st term, we get common ratio, r = = 2

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