Answer:
x ∈ {0, √e}
Step-by-step explanation:
Factoring the equation gives ...
x(2ln(x) -1) = 0
This has two solutions, the values of x that make the factors be zero.
x = 0
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2ln(x) -1 = 0
ln(x) = 1/2 . . . . . . add 1, divide by 2
x = e^(1/2) ≈ 1.64872
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The "zero product rule" is a very powerful aid to solving many equations. While a general polynomial involving terms with logs or exponentials cannot be solved algebraically, sometimes it can be factored in a way that admits solution—as here.
I like a graphing calculator for finding solutions to equations like this.
