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