What is the answer to solvefor x,5x+xln(x)=0 ?

The answer to solvefor x,5x+xln(x)=0 is x= 1/(e^5)

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solvefor x,5x+xln(x)=0

solve for

x, 5 x + x ln (x) = 0

x = \frac{1}{e ^{5}}

Decimal

x = 0.00673 \dots

Solution steps

5 x + x ln (x) = 0

Move

5 x

to the right side

x ln (x) = - 5 x

Move

5 x

to the left side

x ln (x) + 5 x = 0

Factor

x ln (x) + 5 x : x (ln (x) + 5)

x (ln (x) + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or ln (x) + 5 = 0

Solve

ln (x) + 5 = 0 : x = \frac{1}{e ^{5}}

Verify Solutions:

x = 0

False

, x = \frac{1}{e ^{5}}

True

The solution is

x = \frac{1}{e ^{5}}

lo g_{2} (x^{2} - 3) = - 3

ln (3 x) = 2 x - 5

- 1 = 20 lo g_{10} (x)

lo g_{10} (x) - lo g_{10} (x + 3) = - 1

lo g_{100000} (x) = 5^{- 1}

What is the answer to solvefor x,5x+xln(x)=0 ?
The answer to solvefor x,5x+xln(x)=0 is x= 1/(e^5)