# log problem solving

log(1/3)(log3(x))=1

Solve x

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1/3同3都係log下面

### 4 個解答

• 7 年前
最愛解答

http://i1099.photobucket.com/albums/g395/jasoncube...

2013-06-24 16:53:22 補充：

There's something wrong with you calculator?

資料來源： My Maths World
• 7 年前

路過的我實在要提提你,用計數機篤到嘅log係〖log〗_10,唔可以係其他!!

做數要噤:

〖log〗_(1/3)(〖log〗_3(x) )=1

〖log〗_3 (x)=(1/3)^(1)

x=3^(1/3)

x=∛3

所以要check數就要噤:

Subx=∛3,

〖log〗_(1/3)(〖log〗_3(x) )

=〖log〗_(1/3)(〖log〗_3(∛3) )

=〖log〗_(1/3)(〖log〗_3(3^(1/3)) )

=〖log〗_(1/3)(1/3 X〖log〗_3(3) )

∵〖log〗_3(3)=1

∴〖log〗_(1/3)(1/3 X〖log〗_3(3) )

=〖log〗_(1/3)(1/3 X 1 )

∵〖log〗_(1/3) (1/3)=1

∴〖log〗_(1/3)(1/3 X 1 )

=1

僅記計數機篤5到〖log〗_2(2)=1, 但篤到〖log〗_10(10)=1,計數機嘅log底數永遠係10,所以轉base嗰條式就係用黎協助你計log底數5係10嘅數。

(原本喺Word打到〖log〗_(1/3)個樣,貼上黎就變左-_-" ......

如果可上載圖片，我會寫得好D俾你架>.<)

資料來源： 下......我數學嘅累積知識掛~
• 7 年前

正確的，你應該按

log[ log(3^1/3) / log(3)] / log(1/3)

那答案是 1 。

• Tony
Lv 4
7 年前

即係係將x=3^1/3代入log(1/3)(log3(x))出唔到1?

我按到

方法:

[log(3^1/3) / log(3)] / log(1/3) = 1