What is the answer to x^2ln(x)-4ln(x)=0 ?

The answer to x^2ln(x)-4ln(x)=0 is x=1,x=2

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

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

x = 1, x = 2

Solution steps

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

Factor

x^{2} ln (x) - 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_{5} (4 x - 7) = lo g_{5} (x + 5)

lo g_{10} (x^{64}) = - 3

lo g_{6} (7 x + 1) = 2

lo g_{5} (10) = lo g_{10} (x)

lo g_{a} (a^{n}) = n

What is the answer to x^2ln(x)-4ln(x)=0 ?
The answer to x^2ln(x)-4ln(x)=0 is x=1,x=2
Solve for x: x^2ln(x)-4ln(x)=0
The solution is x=1,x=2