What is the answer to 7x^6ln(x)+x^6=0 ?

The answer to 7x^6ln(x)+x^6=0 is x= 1/(\sqrt[7]{e)}

Solve for x: 7x^6ln(x)+x^6=0

The solution is x= 1/(\sqrt[7]{e)}

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7 x^{6} ln (x) + x^{6} = 0

x = \frac{1}{7 e}

Decimal

x = 0.86687 \dots

Solution steps

7 x^{6} ln (x) + x^{6} = 0

Move

x^{6}

to the right side

7 x^{6} ln (x) = - x^{6}

Move

x^{6}

to the left side

7 x^{6} ln (x) + x^{6} = 0

Factor

7 x^{6} ln (x) + x^{6} : x^{6} (7 ln (x) + 1)

x^{6} (7 ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 7 ln (x) + 1 = 0

Solve

7 ln (x) + 1 = 0 : x = \frac{1}{7 e}

Verify Solutions:

x = 0

False

, x = \frac{1}{7 e}

True

The solution is

x = \frac{1}{7 e}

lo g_{3} (6 - x) = 3

lo g_{2} (3 x + 1) = 3

lo g_{5} (x - 5) = 3

y, ln (x) = - ln (y)

4.2 = 4.75 + lo g_{10} (x)

What is the answer to 7x^6ln(x)+x^6=0 ?
The answer to 7x^6ln(x)+x^6=0 is x= 1/(\sqrt[7]{e)}
Solve for x: 7x^6ln(x)+x^6=0
The solution is x= 1/(\sqrt[7]{e)}