What is the answer to 16t^2ln(t)+8t^2=0 ?

The answer to 16t^2ln(t)+8t^2=0 is t= 1/(sqrt(e))

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16t^2ln(t)+8t^2=0

16 t^{2} ln (t) + 8 t^{2} = 0

t = \frac{1}{e}

Decimal Notation

t = 0.60653 \dots

Solution steps

16 t^{2} ln (t) + 8 t^{2} = 0

Move

8 t^{2}

to the right side

16 t^{2} ln (t) = - 8 t^{2}

Move

8 t^{2}

to the left side

16 t^{2} ln (t) + 8 t^{2} = 0

Factor

16 t^{2} ln (t) + 8 t^{2} : 8 t^{2} (2 ln (t) + 1)

8 t^{2} (2 ln (t) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t = 0 or 2 ln (t) + 1 = 0

Solve

2 ln (t) + 1 = 0 : t = \frac{1}{e}

Verify Solutions:

t = 0

False

, t = \frac{1}{e}

True

The solution is

t = \frac{1}{e}

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

2.44 = - lo g_{10} (x)

\frac{( ln ( x ) )}{x} y = 0

(q) = 5 + 10 lo g_{10} (10 + 2 q)

lo g_{10} (2 x) = 1

What is the answer to 16t^2ln(t)+8t^2=0 ?
The answer to 16t^2ln(t)+8t^2=0 is t= 1/(sqrt(e))
Solve for t: 16t^2ln(t)+8t^2=0
The solution is t= 1/(sqrt(e))