What is the answer to x^2ln(x)=(6x-9)ln(x) ?

The answer to x^2ln(x)=(6x-9)ln(x) is x=1,x=3

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x^2ln(x)=(6x-9)ln(x)

x^{2} ln (x) = (6 x - 9) ln (x)

x = 1, x = 3

Solution steps

x^{2} ln (x) = (6 x - 9) ln (x)

Expand

(6 x - 9) ln (x) : 6 x ln (x) - 9 ln (x)

x^{2} ln (x) = 6 x ln (x) - 9 ln (x)

Subtract

6 x ln (x) - 9 ln (x)

from both sides

x^{2} ln (x) - (6 x ln (x) - 9 ln (x)) = 6 x ln (x) - 9 ln (x) - (6 x ln (x) - 9 ln (x))

Simplify

x^{2} ln (x) - 6 x ln (x) + 9 ln (x) = 0

Factor

x^{2} ln (x) - 6 x ln (x) + 9 ln (x) : ln (x) (x^{2} - 6 x + 9)

ln (x) (x^{2} - 6 x + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (x) = 0 or x^{2} - 6 x + 9 = 0

Solve

ln (x) = 0 : x = 1

Solve

x^{2} - 6 x + 9 = 0 : x = 3

Verify Solutions:

x = 1

True

, x = 3

True

The solutions are

x = 1, x = 3

2 lo g_{3} (x - 1) = 4

ln (x^{2}) = ln (12 - x)

lo g_{7} (4) + 3 = lo g_{7} (x)

5 = lo g_{4} (x)

lo g_{10} (x) = - 2.5

What is the answer to x^2ln(x)=(6x-9)ln(x) ?
The answer to x^2ln(x)=(6x-9)ln(x) is x=1,x=3
Solve for x: x^2ln(x)=(6x-9)ln(x)
The solution is x=1,x=3