Question

look at the ttachement and answer th following questions

Answer 1

65.   There is a term on LHS:  Log tan 45° :  = log 1   = 0
           Hence LHS = 0

66.   Tan 0.25 pi = tan 45°  = 1.   its log  is 0.      
67
   LHS = A.     
   take Log₇ A   =     Log₇  (log₇ x)  / Log₇ 5     * log₇ 5
                       = Log₇  (log₇ x)
       so A = log₇ x
=======
68
     Log (2/3)¹°°° =  1000 * Log(2/3) = 1000 * (log 2 - log 3)
           = 1000 (0.3010 - 0.4771)
           = - 176.1

let  X be a fraction.
if logarithm of X  is between 0 and -1, then there is no zero in between the decimal point and the first significant digit after the decimal point.

if Log X  is between -1 and -2 , then there are 1 zeros.
if Log X is between -2 and -3 , there are 2 zeros.

Now, we have Log X = -176.1,  this is in between  -176 and -177.  There are 176 zeros between the decimal point and the first significant digit.