Logarithm problems
- 1. Find the number of digits in 8 10? (Given that log 10 2 = 0.3010)
Options- A. 19
- B. 20
- C. 17
- D. 10 Discuss
Correct Answer: 10
Explanation:
810 = (23)10
? Required answer = [30 log10 2 + 1]
= [30 x 0.3010] + 1
= 9.03 + 1
= 9 + 1
= 10
- 2. Find the no. of digits in 8 57 (given that log 102 = 0.3010)
Options- A. 52
- B. 50
- C. 51
- D. 53 Discuss
Correct Answer: 52
Explanation:
857 = (23)57 = 2171
? Required answer = (171 log10 2 + 1 )
= [171 x 0.3010] + 1 = [51.4710] +1
= 51+1 =52
- 3. If log(x - 5) = log(x) - log(5) and log(y - 6) = log(y) - log(6) then which of the following is correct?
Options- A. x > y
- B. x < y
- C. x = y
- D. Can't say Discuss
Correct Answer: x < y
Explanation:
Given log( x - 5) = log(x) - log(5)
? x -5 = x/5
? x = 25/ 4 ....(i)
Again from question
log(y - 6) = log(y) - log(6)
? y - 6 = y/6
? y = 36/5 ...(ii)
From equations (i) & (ii) x < y
- 4. If log (x + 4) = log(4) + log(x) and log (x + 6) = log (6) then which of the following correct?
Options- A. x = y
- B. x < y
- C. x > y
- D. Can't say Discuss
Correct Answer: x > y
Explanation:
Given log (x + 4) = log(4) + log(x)
? x + 4 = 4x
? x = 4/3
Similarly y = 5/4
? x > y
- 5. If a x = b, b y = c, c z = a, then the value of xyz is?
Options- A. 0
- B. 1
- C. 2
- D. 4 Discuss
Correct Answer: 1
Explanation:
? ax = b
? loga b = x
? by = c
? logb c = y
? cz = a
? logc a = z
? xyz = logab x logbc x logca = 1
- 6. If log xy = 100 and log 2x = 10 then the value of y is?
Options- A. 210
- B. 21000
- C. 2100
- D. 210000 Discuss
Correct Answer: 21000
Explanation:
logxy =100, log2x = 10
? log y / log x = 100 and log x / log 2 = 10
? log y / log 2 = 100 x 10 = 1000
? log2y = 1000
? y = 21000
- 7. If log x4 = 0.4 then the value of x is?
Options- A. 4
- B. 16
- C. 1
- D. 32 Discuss
Correct Answer: 32
Explanation:
logx4 = log 4 / log x = 2/5
? 2log2 / log x = 2/5
? log x =5log 2 = log 25
? log x = log 32
? x = 32
- 8. If log 1227 =a then log 616 is?
Options- A. 4(3 - a) / 3 + a
- B. 4(3 + a) / 3 - a
- C. 3 + a / 4(3 - a)
- D. 3 - a / 4(3 + a) Discuss
Correct Answer: 4(3 - a) / 3 + a
Explanation:
? log1227 = a
? log 27 / log 12 = a
? a log 12 = log 33
? a log ( 3 x 4 ) = 3 log 3
? a[log 3 + log 4] = 3 log 3
? a log 4 + a log 3 = 3 log 3
? a log 22 = ( 3 - a) log 3
? 2a log 2 = (3 - a) log 3
? log 2 / log 3 = (3 - a) / 2a
Now log616 = log16 / log 6 = log 24 / log (2 x 3) = 4 log 2 / ( log 2 + log 3)
= [4 (log 2 / log 3)] / [(log 2 / log 3) + 1]
= 4[(3 - a) / 2a] / [{(3 - a) / 2a } + 1]
= 4(3 - a) / (3 + a)
- 9. If log (0.57) = 1756, then the value of log 57 + log (0.57) 3 + log ? 0.57 is?
Options- A. 0.902
- B. 1.902
- C. 1.146
- D. 2.146 Discuss
Correct Answer: 0.902
Explanation:
Given Exp.
= log (57 x 100 / 100) + 3log(0.57) + 1/2log(0.57)
= log (0.57) + log 102 + 3log(0.57) +1/2log (0.57)
= (1 + 3 + 1/2) log(0.57) + 2 [? log102 = 2]
= (4.5 x 1.756) + 2 = 4.5 x (-1 + 0.756) + 2
= 3.402 - 4.5 + 2
= 0.902
- 10. (log tan1°. log tan2° ............. log tan50°) is?
Options- A. 0
- B. 1
- C. 2
- D. - 1 Discuss
Correct Answer: 0
Explanation:
? log tan 45 = log 1 = 0
Hence, Whole Expression = (something) x zero
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.