求解5^x=x^5,（5的x次方=x的5次方），并求详细过程啊

是我题目
Compare the functions f(x) = x5 and g(x) = 5x
by graphing both functions in several viewing rectangles.
(Enter your answers as a comma-separated list, y) = 【 】（larger x-value)
Which function grows more rapidly when x is large，f(x) B, y) = 【 】 (smaller x-value)
(x. Round any decimal answers
to one decimal place?
A.)
(x. Find all
points of intersection of the graphs correct to one decimal place

就是求f（x）=5^x-x^5的零点个数
先目测出x=5是一个解
再求证f（x）单调递增 与x轴只有一个交点
那么x=5就是唯一解
不然的话就多解（我自己没证过）

x=5

去以5为底的对数，5^x=x^5化为x/5=log以5为底x的对数，再画图像。 答案：x=5（唯一解） 再看看别人怎么说的。