What is the answer to 6x^2ln(x)=24ln(x) ?

The answer to 6x^2ln(x)=24ln(x) is x=1,x=2

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6x^2ln(x)=24ln(x)

6 x^{2} ln (x) = 24 ln (x)

x = 1, x = 2

Solution steps

6 x^{2} ln (x) = 24 ln (x)

Divide both sides by

6

\frac{6 x ^{2} ln ( x )}{6} = \frac{24 ln ( x )}{6}

Simplify

ln (x) x^{2} = 4 ln (x)

Move

4 ln (x)

to the left side

ln (x) x^{2} - 4 ln (x) = 0

Factor

ln (x) x^{2} - 4 ln (x) : ln (x) (x^{2} - 4)

ln (x) (x^{2} - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (x) = 0 or x^{2} - 4 = 0

Solve

ln (x) = 0 : x = 1

Solve

x^{2} - 4 = 0 : x = 2, x = - 2

Verify Solutions:

x = 1

True

, x = 2

True

, x = - 2

False

The solutions are

x = 1, x = 2

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

14 - 12.05 = - lo g_{10} (x)

lo g_{4} (2 - x) = lo g_{4} (- 5 x - 18)

x, 2 x - 1 = e^{l n (x) 2}

lo g_{10} (x) = 0.1445

What is the answer to 6x^2ln(x)=24ln(x) ?
The answer to 6x^2ln(x)=24ln(x) is x=1,x=2
Solve for x: 6x^2ln(x)=24ln(x)
The solution is x=1,x=2