# TA Exam Maths Topic Logarithm: Formulas and Sample Problems

In this article we will share TA Exam Maths Topic Logarithm: Formulas and Sample Problems

# Territorial Army 2 2017 Exam Mock Test Series ## TA Exam Maths Topic Logarithm: Formulas and Sample Problems If a is a positive real number, other than 1 and ab = x, then we write:

b = logax and we say that the value of log x to the base a is b.

Properties of Logarithms: Q. If log 27 = 1.431, then the value of log 9 is:
 A. 0.934 B. 0.945 C. 0.954 D. 0.958

log 27 = 1.431

log (33 ) = 1.431

3 log 3 = 1.431

log 3 = 0.477

log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.

Q. If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
 A. 1 B. 3 C. 5 D. 10

log10 5 + log10 (5x + 1) = log10 (x + 5) + 1

log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10

log10 [5 (5x + 1)] = log10 [10(x + 5)]

5(5x + 1) = 10(x + 5)

5x + 1 = 2x + 10

3x = 9

x = 3.

Q. If log 2 = 0.30103, the number of digits in 264 is:
 A. 18 B. 19 C. 20 D. 21

 log (264) = 64 x log 2 = (64 x 0.30103) = 19.26592

Its characteristic is 19.

Hence, then number of digits in 264 is 20.

Q. If log (a/b)+log(b/a) = log (a + b), then:
 A. a + b = 1 B. a – b = 1 C. a = b D. a2 – b2 = 1

log (a/b)+log(b/a) = log (a + b)

 log (a + b) = log a x b = log 1. b a

So, a + b = 1.

Q. The value of log2 16 is:
A.
 1 8
B. 4
C. 8
D. 16

Let log2 16 = n.

Then, 2n = 16 = 24          n = 4.

log2 16 = 4. #### Ashutosh

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