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.

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

Correct Answer: 1

Correct Answer: 4

Explanation:

log 2 3 144 = 4 

Correct Answer: (1+2m)/2

Explanation:

log 49 28 = 1 2 log 7 7 × 4

 

= 1 2 + 1 2 2 log 7 2
= 1 2 + log 7 2
=  1 2 + m
=  1 + 2 m 2.

Correct Answer: 256/81

Correct Answer: 32

Correct Answer: a + b = 1

Explanation:

 

i f log a b + log b a = log a + b , t h e n

log a + b = log a b × b a = log 1

 

so, a+b=1

Correct Answer: p > q

Explanation:

k l > k + 1 l + 1 for (k,l) > 0 and  k > l 

 

 

 

Let     k = x+1    and   l = x

 

 

 

Therefore,  x + 1 x > ( x + 1 ) + 1 ( x ) + 1

 

 

 

 (x + 1) > x

 

 

 

Therefore,  log ( x + 1 ) log ( x ) > log ( x + 2 ) log ( x + 1 )

 

 

 

? log x x + 1 > log x + 1 x + 2

Correct Answer: -5

Explanation:

log (0.0000134). Since there are four zeros between the decimal point and
the first significant digit, the characteristic is ?5.

Correct Answer: 3/2

Explanation:

  $$\begin{gathered} = log 3 3 + log 2 3 + log 10 3 log 10 × 3 × 2 2 \\ \end{gathered}$$ 

 

 

 

= log 3 3 1 2 + log 2 3 + log 10 3 1 2 log ( 10 × 3 × 2 2 )  

 

 

 

 

 

 

 

= 1 2 log 3 3 + 3 log 2 + 1 2 log 10 3 log 10 + log 3 + log 2 2  

 

 

 

 

 

 

 

= 3 2 log 3 + 2 log 2 + log 10 log 3 + 2 log 2 + log 10 =  3 2