What is the answer to x^x(ln(x)+1)=0 ?

The answer to x^x(ln(x)+1)=0 is x= 1/e

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x^x(ln(x)+1)=0

x^{x} (ln (x) + 1) = 0

x = \frac{1}{e}

Decimal Notation

x = 0.36787 \dots

Solution steps

x^{x} (ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x^{x} = 0 or ln (x) + 1 = 0

Solve

x^{x} = 0 :

No Solution for

x \in R

Solve

ln (x) + 1 = 0 : x = \frac{1}{e}

Verify Solutions:

x = \frac{1}{e}

True

The solution is

x = \frac{1}{e}

4^{x^{2}} \cdot 4^{5 x - 3} = 64

27 m^{3 x} = 1

2^{c} = 65536

7^{x^{2} - 4} - 1 = 0

20 = 25 e^{- 0.00012 t}