What is the answer to 20x^3ln(x)+9x^3=0 ?

The answer to 20x^3ln(x)+9x^3=0 is x= 1/(e^{9/20)}

Solve for x: 20x^3ln(x)+9x^3=0

The solution is x= 1/(e^{9/20)}

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20 x^{3} ln (x) + 9 x^{3} = 0

x = \frac{1}{e ^{\frac{9}{20}}}

Decimal

x = 0.63762 \dots

Solution steps

20 x^{3} ln (x) + 9 x^{3} = 0

Move

9 x^{3}

to the right side

20 x^{3} ln (x) = - 9 x^{3}

Move

9 x^{3}

to the left side

20 x^{3} ln (x) + 9 x^{3} = 0

Factor

20 x^{3} ln (x) + 9 x^{3} : x^{3} (20 ln (x) + 9)

x^{3} (20 ln (x) + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 20 ln (x) + 9 = 0

Solve

20 ln (x) + 9 = 0 : x = \frac{1}{e ^{\frac{9}{20}}}

Verify Solutions:

x = 0

False

, x = \frac{1}{e ^{\frac{9}{20}}}

True

The solution is

x = \frac{1}{e ^{\frac{9}{20}}}

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

- lo g_{10} (x) = 3

ln (5 x) = 2 x - 1

ln (x) = 7

ln ((x + 1)^{2}) = 2

What is the answer to 20x^3ln(x)+9x^3=0 ?
The answer to 20x^3ln(x)+9x^3=0 is x= 1/(e^{9/20)}
Solve for x: 20x^3ln(x)+9x^3=0
The solution is x= 1/(e^{9/20)}