logarithm aptitude questions – Free Online Questions and Answers

Which of the following statements is not correct?

Answer: Option B

Explanation:

(a) Since log_a a = 1, so log₁₀ 10 = 1.

(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

log (2 + 3) log (2 x 3)

(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

So, (b) is incorrect.

If log 2 = 0.3010 and log 3 = 0.4771, the value of log₅ 512 is:

A.	2.870	B.	2.967
C.	3.876	D.	3.912

Answer: Option C

Explanation:

log₅ 512

=	log 512
	log 5

=	log 2⁹
	log (10/2)

=	9 log 2
	log 10 – log 2

=	(9 x 0.3010)
	1 – 0.3010

=	2.709
	0.699

=	2709
	699

= 3.876

log 8	is equal to:
log 8

Answer: Option C

Explanation:

log 8	=	log (8)^1/2	=	log 8	=	1	.
log 8		log 8		log 8		2

If log 27 = 1.431, then the value of log 9 is:

A.	0.934	B.	0.945
C.	0.954	D.	0.958

Answer: Option C

Explanation:

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.

If log	a	+	log	b	= log (a + b), then:
	b			a

A.	a + b = 1	B.	a – b = 1
C.	a = b	D.	a² – b² = 1

Answer: Option A

Explanation:

log	a	+ log	b	= log (a + b)
	b		a

log (a + b) = log		a	x	b		= log 1.
		b		a

So, a + b = 1.