SOLUTION: The product of all the real roots of x^log(base 10)x = 10 is

Question 1153084: The product of all the real roots of x^log(base 10)x = 10 is
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20855)   (Show Source): You can put this solution on YOUR website!

......take log of both sides

solutions for this log:
or -> since log, disregard negative solution
........since

since you have only solution, product is

Answer by ikleyn(53763)   (Show Source): You can put this solution on YOUR website!
.

You are given this equation = 10. Take log(base 10) from both sides. You will get = 1, or = 1. Take the square root from both sides = +/- 1. Case 1. = 1. It implies x = 10. Case 2. = -1. It implies x = . ANSWER. The given equation has 2 (two, TWO) solutions x = 10 and x = . +------------------------------------------------------------------+ | The product of the roots (as the question asks) is 10* = 1. | +------------------------------------------------------------------+ To check, I made two plots with different x-scales of the function y = . See below. Plot y = (red) and y = 10 (green). Plot y = (red) and y = 10 (green).

In the post by @MathLover1, the solution   x =   is lost.

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