What is the answer to 42x^5ln(x)+13x^5=0 ?

The answer to 42x^5ln(x)+13x^5=0 is x= 1/(e^{13/42)}

Solve for x: 42x^5ln(x)+13x^5=0

The solution is x= 1/(e^{13/42)}

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42 x^{5} ln (x) + 13 x^{5} = 0

x = \frac{1}{e ^{\frac{13}{42}}}

Decimal

x = 0.73379 \dots

Solution steps

42 x^{5} ln (x) + 13 x^{5} = 0

Move

13 x^{5}

to the right side

42 x^{5} ln (x) = - 13 x^{5}

Move

13 x^{5}

to the left side

42 x^{5} ln (x) + 13 x^{5} = 0

Factor

42 x^{5} ln (x) + 13 x^{5} : x^{5} (42 ln (x) + 13)

x^{5} (42 ln (x) + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 42 ln (x) + 13 = 0

Solve

42 ln (x) + 13 = 0 : x = \frac{1}{e ^{\frac{13}{42}}}

Verify Solutions:

x = 0

False

, x = \frac{1}{e ^{\frac{13}{42}}}

True

The solution is

x = \frac{1}{e ^{\frac{13}{42}}}

ln (\frac{x}{e}) = 2

y, lo g_{3} (x) = y + 1

lo g_{x} (11) = - 1

lo g_{10} (x) + lo g_{10} (4) = 2

1.5 = - lo g_{10} (x)

What is the answer to 42x^5ln(x)+13x^5=0 ?
The answer to 42x^5ln(x)+13x^5=0 is x= 1/(e^{13/42)}
Solve for x: 42x^5ln(x)+13x^5=0
The solution is x= 1/(e^{13/42)}