首數與尾數問題
3-5-2
1. x x = a ?10n 1 a < 10 n log x = n + log a ( 0 log a < 1) n log x log a log x
2. x log x = n + log a 0 log a < 1 n (1) log x n n 0 x n +1 x = 123000 x = 1.23?105 log x = 5 + log1.23 log x 5 (2) log x -n n > 0 x n 0 x = 0.00123 x = 1.23?10-3
log x = (-3) + log1.23
log x ?3 (3) log a 1 2
0 log a < 1
1
1 250 ( log 2 0.3010 log3 0.4771) Ans
log 250 = 50 ? log 2 = 50 ? (0.3010) = 15.05 = 15 + 0.05 log1 < 0.05 < log 2
250 16 1
2
3 5
30
0
0
Ans
log
3 5
30
=
30 ? log
3 5
=
30 ? (log3
-
log 5)
=
30 ?
( -0.2219 )
=
-6.657
=
-7
+
0.343
log 2 < 0.343 < log3
3 5
30
7
0
0
2
3 (5)n < 1 n
6 1000
Ans
log(5)n < log 1
6
1000
n log 5 < log 1
6 1000
n(log5 - log 6) < -3
n > 3 = 37.925
0.0791
n 38
2
4 4720 34 (1) 4714 (2) 47-5 0
Ans 4720 34 33 log 4720 < 34
33 20log 47 < 34 1.65 log 47 ................
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