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.

log 2 3 144 = 4 

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

T i m e = 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 = ( 100 + x ) 25 2 

? X=150m

            =>  log 60 ( 3 * 4 * 5 )

                              =>      log 60 60

                                   = 1

 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 3is 13.

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