What is the answer to 0=12x^2ln(x)+7x^2 ?

The answer to 0=12x^2ln(x)+7x^2 is x= 1/(e^{7/12)}

Solve for x: 0=12x^2ln(x)+7x^2

The solution is x= 1/(e^{7/12)}

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0 = 12 x^{2} ln (x) + 7 x^{2}

x = \frac{1}{e ^{\frac{7}{12}}}

Decimal

x = 0.55803 \dots

Solution steps

0 = 12 x^{2} ln (x) + 7 x^{2}

Switch sides

12 x^{2} ln (x) + 7 x^{2} = 0

Move

7 x^{2}

to the right side

12 x^{2} ln (x) = - 7 x^{2}

Move

7 x^{2}

to the left side

12 x^{2} ln (x) + 7 x^{2} = 0

Factor

12 x^{2} ln (x) + 7 x^{2} : x^{2} (12 ln (x) + 7)

x^{2} (12 ln (x) + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 12 ln (x) + 7 = 0

Solve

12 ln (x) + 7 = 0 : x = \frac{1}{e ^{\frac{7}{12}}}

Verify Solutions:

x = 0

False

, x = \frac{1}{e ^{\frac{7}{12}}}

True

The solution is

x = \frac{1}{e ^{\frac{7}{12}}}

x^{3} + 4 x^{3} ln (x) = 0

lo g_{10} (2 x - 5) = 0

lo g_{0.2} (3 x - 1) = - 3

lo g_{\frac{1}{4}} (x + 4) = - 1

lo g_{2} (x + 3) = 6

What is the answer to 0=12x^2ln(x)+7x^2 ?
The answer to 0=12x^2ln(x)+7x^2 is x= 1/(e^{7/12)}
Solve for x: 0=12x^2ln(x)+7x^2
The solution is x= 1/(e^{7/12)}