(log2 3+log4 9+....+以2的n次方为底3的n次方的对数)乘以log9 8的n次方根

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2025-06-28 10:45:30
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回答1:

(log2
3+log4
9+....+以2的n次方为底3的n次方的对数)乘以log9
8的n次方根
[利用对数的换底公式]
=
[ln3/ln2
+
2ln3/(2ln2)
+
...
+
nln3/(nln2)][nln8/(2ln3)]
=
[ln3/ln2][1
+
1
+
...
+
1][3nln2/(2ln3)]
=
n[3n/2]
=
3n^2/2