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logarithm

[匿名]

2012-02-23 4:44 am

solve sin(x)=log(x) when sin(x) is in radian and log(x) is in 10-base

find there are how many solutions and what it is?step please
It is just a Form 4 question

更新1:

F4 trigonometry teach radian already, you may also give the method to find the exact solution, thanks

更新2:

Also, why 1.5 cycle must only have 3 solutions??need plot graph to find it??? why 180 degree to 360 degree have no solution??need plot graph to find it???

回答 (1)

用戶10012

2012-02-23 6:01 am

✔ 最佳答案

Since x must be positive and sin x < 1, so log x must be < 1 for a solution. So 1 < x < 10 in radian.
In degree, 57.3 < x < 573 which is about 1.5 cycles. So there are 3 solutions.
(1 between 90 and 180 degree, 2 between 360 and 540 degrees).
For exact solution,I don't think this is Form 4 question. By the way, Form 4 teaching radian??

2012-02-22 22:08:53 補充：
From wolfram|alpha, answers are : 2.696, 7.328 and 8.264 radians. Or 154, 420 and 473 degrees.

2012-02-23 08:32:25 補充：
Remark : Simplest method to find the no. of solution is by sketching the graph of sin x and log x to see the intersecting points. 2. No solution between 180 and 360 because sin 180 to sin 360 is negative.

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