What is the answer to ln(x)-6x^2ln(x)=-5xln(x) ?

The answer to ln(x)-6x^2ln(x)=-5xln(x) is x=1

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ln(x)-6x^2ln(x)=-5xln(x)

ln (x) - 6 x^{2} ln (x) = - 5 x ln (x)

x = 1

Solution steps

ln (x) - 6 x^{2} ln (x) = - 5 x ln (x)

Move

5 x ln (x)

to the left side

ln (x) - 6 x^{2} ln (x) + 5 x ln (x) = 0

Factor

ln (x) - 6 x^{2} ln (x) + 5 x ln (x) : ln (x) (1 - 6 x^{2} + 5 x)

ln (x) (1 - 6 x^{2} + 5 x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (x) = 0 or 1 - 6 x^{2} + 5 x = 0

Solve

ln (x) = 0 : x = 1

Solve

1 - 6 x^{2} + 5 x = 0 : x = - \frac{1}{6}, x = 1

Verify Solutions:

x = 1

True

, x = - \frac{1}{6}

False

The solution is

x = 1

x, y^{2} + ln (x y) = 2

3 lo g_{2} (x) = 5

ln (x^{8}) - 9 ln (x) = 6

- 8 lo g_{10} (b) = - 64

3 lo g_{2} (x^{2} + 6 x) + 5 = 17

What is the answer to ln(x)-6x^2ln(x)=-5xln(x) ?
The answer to ln(x)-6x^2ln(x)=-5xln(x) is x=1
Solve for x: ln(x)-6x^2ln(x)=-5xln(x)
The solution is x=1