The value of 1log360+1log460+1log560is 0 1 5 60 => log 60 ( 3 * 4 * 5 ) => log 6

1. A fast moving superfast express crosses another pasenger train in 20 seconds. The speed of faster train is 72 km/hr and speeds of slower train is 27 km/h. Also the length of faster ntrain is 100m, then find the length of the slower train if they are moving in the same direction.
Options
A. 100 m
B. 125 m
C. 150 m
D. 175 m

Discuss

Correct Answer: 150 m

Explanation:

$T i m e = \frac{S u m o f l e n g t h o f t h e t w o t r a i n s}{D i f f e r e n c e i n s p e e d s}$

$20 = \frac{(100 + x)}{\frac{25}{2}}$

$?$ X=150m

2. If log 64 = 1.8061, then the value of log 16 will be (approx)?
Options
A. 1.9048
B. 1.2040
C. 0.9840
D. 1.4521

Discuss

Correct Answer: 1.2040

Explanation:

Given that, log 64 = 1.8061

i.e $\log (4^{3}) = 1.8061$

--> 3 log 4 = 1.8061

--> log 4 = 0.6020

--> 2 log 4 = 1.2040

$? \log (4^{2}) = 1.2040$

Therefore, log 16 = 1.2040

3. If logxl+m-2n = logym+n-2l = logzn+l-2m , then xyz is equal to
Options
A. 0
B. 1
C. lmn
D. 2

Discuss

Correct Answer: 1

4. Find the logarithm of 144 to the base 23 :
Options
A. 2
B. 4
C. 8
D. None of these

Discuss

Correct Answer: 4

Explanation:

$\log_{2 \sqrt{3}} (144) = 4$

5. If log72 = m, then log4928 is equal to ?
Options
A. 1/(1+2m)
B. (1+2m)/2
C. 2m/(2m+1)
D. (2m+1)/2m

Discuss

Correct Answer: (1+2m)/2

Explanation:

$\log_{49} (28) = \frac{1}{2 \log_{7} (7 � 4)}$

= $\frac{1}{2} + \frac{1}{2} (2 \log_{7} (2))$
= $\frac{1}{2} + \log_{7} (2)$
= $\frac{1}{2} + m$
= $\frac{1 + 2 m}{2}$ .

6. If log8x = 313 then find the value of x?
Options
A. 25
B. 32
C. 37
D. None of these

Discuss

Correct Answer: 32

7. What is the number of digits in 333 ? Given that log3 = 0.47712?
Options
A. 12
B. 13
C. 14
D. 15

Discuss

Correct Answer: 13

Explanation:

Let $L e t x = (3^{3^{3}})$ = ${(3^{3})}^{3}$

Then, $\log (x) = 3^{3} \log (3)$

= 27 x 0.47712 = 12.88224

Since the characteristic in the resultant value of log x is 12

$?$ The number of digits in x is (12 + 1) = 13

Hence the required number of digits in $3^{3^{3}}$ is 13.

8. if logab+logba=loga+b,then
Options
A. a + b = 1
B. a - b = 1
C. a = b
D. ab=1

Discuss

Correct Answer: a + b = 1

Explanation:

$i f \log \frac{a}{b} + \log \frac{b}{a} = \log (a + b), t h e n$

$\log (a + b) = \log (\frac{a}{b} � \frac{b}{a}) = \log 1$

so, a+b=1

9. The least value of the expression 2log10x - logx1100 for x>1 is:
Options
A. 2
B. 3
C. 4
D. 5

Discuss

Correct Answer: 4

Explanation:

Hence the least value of is 4

10. Solve the equation 122x+1 = 1 ?
Options
A. -1/2
B. 1/2
C. 1
D. -1

Discuss

Correct Answer: -1/2

Explanation:

Rewrite equation as ${(\frac{1}{2})}^{2 x + 1} = {(\frac{1}{2})}^{0}$

Leads to 2x + 1 = 0

Solve for x : x = -1/2

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