The number of solutions of the equation logx2x2+40log4xx-14log16xx3=0 is: 0 1 2

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Question
The number of solutions of the equation logx2x2+40log4xx-14log16xx3=0 is:
Options
A. 0
B. 1
C. 2
D. 3

Correct Answer

Logarithm problems

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1. The value of log2log5625 is :
Options
A. 2
B. 5
C. 10
D. 15

Discuss

Correct Answer: 2

2. The value of x satisfying the following relation: log12x = log23x-2
Options
A. 1/3
B. -1/3
C. 3
D. None of these

Discuss

Correct Answer: None of these

Explanation:

But at x=-1/3, log x is not defined.

The only admissible value of x is 1.

3. Find x if log1218 = log24x + 1. log24x+1 + 4
Options
A. 0
B. 1
C. 2
D. None of these

Discuss

Correct Answer: 0

Explanation:

By trial and error method, when we substitute

x = 0

Both LHS and RHS are equal.

4. If log330 = 1a and log530=1b then the value of 3log302 is:
Options
A. 3(1+a+b)
B. 2(1-a-b)
C. 3(1-a-b)
D. 3(1+a-b)

Discuss

Correct Answer: 3(1-a-b)

5. The value of 13log10125 - 2log104 + log1032 :
Options
A. 0
B. 1
C. 2
D. 4/5

Discuss

Correct Answer: 1

6. If a, b, c be the pth, qth and rth terms of a GP then the value of (q-r) log a + (r-p) log b + (p-q) log c is :
Options
A. 0
B. 1
C. -1
D. pqr

Discuss

Correct Answer: 0

Explanation:

7. The value of log3437 is:
Options
A. 1/3
B. -3
C. -1/3
D. 3

Discuss

Correct Answer: 1/3

Explanation:

$\log_{343} (7) \log_{7^{3}} (7) \frac{1}{3} \log_{7} (7) W e k n o w t h a t l o g_{x} (x) = 1 = > \frac{1}{3}$

8. If 5x - 17 = -x + 7, then x = ?
Options
A. 4
B. 5
C. 7
D. 9

Discuss

Correct Answer: 4

Explanation:

Given equation 5x-17 = -x+7

Add 1x to each side of the equation

5x-17+x = -x+7+x

6x=24

x=4

9. If A = log321875 and B = log2432187 , then which one of the following is correct?
Options
A. A
B. A=B
C. A>B
D. can't be determined

Discuss

Correct Answer: A=B

Explanation:

Given $A = \frac{\log_{3} (2187)}{5} a n d B = \log_{243} (2187)$

$B = \log_{3^{5}} (2187) = \frac{\log_{3} (2187)}{5}$

=> A

Therefore, A = B

10. (51+ 52 + 53 + ... + 100) =?
Options
A. 2525
B. 2975
C. 3225
D. 3775

Discuss

Correct Answer: 3775

Explanation:

This is an A.P. in which a = 51, l = 100 and n = 50.

∴Sum =	n	(a + l)	=	50	x (51 + 100) = (25 x 151) = 3775.
	2			2

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The number of solutions of the equation logx2x2+40log4xx-14log16xx3=0 is:

Logarithm problems

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