數學問題(應該係F.4既問題)

Question

2^x = x^3
(即係: 2的x次方等於x的3次方)
求x.

其實我並不肯定是中四的問題...
只是我一個朋友的弟弟(中四)問的一個問題......

Answer 1

2^x = x^3
這題目暫時沒有直接解的方法，所以只可以用圖解的方法計算
設
y = 2^x – x^3
繪出這圖線的圖解，找出它和x軸的交點後計算結果

以下的結果是用圖表及電腦協助而求出的結果
x = 1.37346711969616
及
x = 9.9395351414269

Answer 2

Is this really a form 4 level question?

If the unknown x is in the index, you can try applying logarithm to both sides of the equation.
2^x = x^3
log 2^x = log x^3
x log 2 = 3 log x
which would need to be solved by numerical methods to approximate the solution.

You can try to plot the graphs of the 2 equations:
{ y = 2^x
{ y = x^3
and you will see there is one solution between 1 and 2

Answer 3

這是一條俾電腦做的數而不是用人腦做的數。絕不會是F4的數。