Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Which of the following is not true?

A) \( \Large \frac{1}{log_{3} \pi } + \frac{1}{log_{4} \pi }>2 \)
B) \( \Large log_{3}5 \)
C) \( \Large \sqrt{8x} = \frac{10}{3} => x = 16 \)
D) \( \Large log_{x} \left(a^{2}+1\right)<0 \), (a?0) then 0

Correct Answer:



C) \( \Large \sqrt{8x} = \frac{10}{3} => x = 16 \)

Description for Correct answer:

(A) \( \Large \frac{1}{log_{3} \pi } + \frac{1}{log_{4} \pi } = log_{ \pi }3 + log_{ \pi }4 = log_{ \pi} 12 > 2\)

\( \Large 12 > \pi ^{2} \)

(B) \( \Large log_{3}5 \) is an irrational number

(C) \( \Large log\sqrt{8}x = \frac{10}{3} => x = \left(\sqrt{8}\right)^{\frac{10}{3}} = 2^{5} \)

\( \Large x = 32 \)

(D) \( \Large log_{x} \left(a^{2}+1\right) < 0, a ≠ 0 => a^{2}+1 > 1 \)

So, log is negative

Hence, base is (0, 1).

Part of solved Logarithms questions and answers : >> Elementary Mathematics >> Logarithms

Comments

Similar Questions

1). If \( \Large y = \frac{1}{a^{1-log ax}} \) and \( \Large z = \frac{1}{a^{1+log_{a}y}} \) then x is equal to:

A). \( \Large \frac{1}{a^{1+log_{a}z}} \)

B). \( \Large \frac{1}{a^{z+log_{a}z}} \)

C). \( \Large \frac{1}{a^{1-log_{a}z}} \)

D). none of these

2). The least value of n in order that the sum of first n terms of an infinite series \( \Large 1 + \frac{3}{4} + \left(\frac{3}{4}\right)^{2} + \left(\frac{3}{4}\right)^{3}+ .... \) should differ from the sum of the series by less then \( \Large 10^{-6} \) is
[\( \Large\ Given\ log_{10}2=0.30103, log_{10}3=0.47712 \)]

A). 14

B). 27

C). 53

D). 57

3). Solution of the equation \( \Large x log^{x^{2}} = log3 \left(x+y\right) \) and \( \Large x^{2}+y^{2} = 65 \) is:

A). x = 8, y = 1

B). x = 1, y = 8

C). (x=8, y=1); (x=1, y=8)

D). none of the above

4). The identity \( \Large log_{a}n\ log_{b}n\ +\ log_{b}n\ log_{c}n\ +\ log_{c}n\ log_{a}n \) ls:

A). \( \Large \frac{log_{a}n\ log_{b}n\ log_{c}n}{log_{abc}n} \)

B). \( \Large \frac{log_{abc}n}{log_{a}n} \)

C). \( \Large \frac{log_{b}n}{log_{abc}n} \)

D). none of these

5). The least value of the expression \( \Large 2\ log_{10}x\ -\ logx\ \left(0.01\right) \) for x > 1, is:

A). 10

B). 2

C). -0.01

D). none of the above

6). The angle of elevation of the top of a tower at a point on the ground is \( \Large 30 ^{\circ} \). If on walking 20m towards the tower the angle of elevation becomes \( \Large 60 ^{\circ} \) then the heights of the tower is:

A). 10 m

B). \( \Large \frac{10}{\sqrt{3}} m \)

C). \( \Large 10\sqrt{3} m \)

D). None of these

7). When the elevation of sun changes from \( \Large 45 ^{\circ} \) to \( \Large 30 ^{\circ} \) the shadow of a tower increases by 60 m, The height of the tower is:

A). \( \Large 30\sqrt{3} m \)

B). \( \Large 30 \left(\sqrt{2} + 1\right) m \)

C). \( \Large 30 \left(\sqrt{3} - 1\right) m \)

D). \( \Large 30 \left(\sqrt{3} + 1\right) m \)

8). A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \( \Large 60 ^{\circ} \) when he retire 40 m from the bank he finds the angle to be \( \Large 30 ^{\circ} \). The breadth of the river is:

A). 20 m

B). 40 m

C). 30 m

D). 60 m

9). A flag-staff is upon the top of a building. If at a distance of 40 m from the base of building the angles of elevation of the tapes of the flag-staff and building are \( \Large 60 ^{\circ} \) and \( \Large 30 ^{\circ} \) respectively, then the height of the flag-staff is:

A). 46.19 m

B). 50 m

C). 25 m

D). none of these

10). A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, the distance between the two houses is:

A). 48 m

B). 36 m

C). 54 m

D). 72 m