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This mock test of Test: Logarithm- 5 for CAT helps you for every CAT entrance exam.
This contains 15 Multiple Choice Questions for CAT Test: Logarithm- 5 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Solution:

QUESTION: 2

If log 2 = .301, find the number of digits in (125)^{25}.

Solution:

logy = 25 log 125

= 25 [log 1000 - 3 log 2]

= 25 x (2.097)

= 52 +

Hence 53 digits.

QUESTION: 3

Solution:

(75/35) x (49/25) x (jc/105) x (25/13) = 1 ⇒ x = 13

QUESTION: 4

Which one of the following is true

Solution:

QUESTION: 5

Solution:

x = (16/15) x (25^{5}/24^{5}) x (81^{3}/80^{3}) None of these is correct.

QUESTION: 6

Find the value of the logarithmic expression in the questions below.

Solution:

log (a^{n}b^{n}c^{n}/a^{n}b^{n}c^{n}) = log 1 = 0

QUESTION: 7

Solution:

QUESTION: 8

log_{2} (9 - 2^{X}) = 10^{log (3-x)} Solve for x.

Solution:

For x = 0, we have LHS

Log_{2} 8 = 3.

RHS: 10^{log3} = 3.

We do not get LHS = RHS for either x = 3 or x = 6.

Thus, option (a) is correct.

QUESTION: 9

Which one of the following is true

Solution:

QUESTION: 10

log (x - 13) + 3 log 2 = log (3x + 1)

Solution:

QUESTION: 11

log . 0867 = ?

Solution:

Log 0.0867 = log (8.67/100) = log 8.67 - log 100 Log 8.67 - 2

QUESTION: 12

log_{3}x = 1/2

Solution:

x = 3^{1/2} = √3 .

QUESTION: 13

If log_{10}a = b, find the value of 10^{3b} in terms of a.

Solution:

log_{10}a = b ⇒ 10^{b} = a ⇒ By definition of logs.

Thus 10^{3b} = (10^{b})^{3} = a^{3}.

QUESTION: 14

log (x^{2} - 6x + 6) = 0

Solution:

QUESTION: 15

Find x If logx = log 1.5 + log 12

Solution:

log x = log 18 ⇒ x = 18

### Logarithm Formula

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