What is the answer to 8ln(x^2)=x ?

The answer to 8ln(x^2)=x is x=-16\W_{0}(1/16),x=-16\W_{0}(-1/16),x=-16\W_{-1}(-1/16)

Solve for x: 8ln(x^2)=x

The solution is x=-16\W_{0}(1/16),x=-16\W_{0}(-1/16),x=-16\W_{-1}(-1/16)

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8 ln (x^{2}) = x

x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

Decimal Notation

x = - 0.94277 \dots, x = 1.06910 \dots, x = 67.36107 \dots

Solution steps

8 ln (x^{2}) = x

Divide both sides by

8

ln (x^{2}) = \frac{x}{8}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x^{2})} = e^{\frac{x}{8}}

Simplify

e^{l n (x^{2})} : x^{2}

x^{2} = e^{\frac{x}{8}}

Solve

x^{2} = e^{\frac{x}{8}} : x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

Verify Solutions:

x = - 16 W_{0} (\frac{1}{16})

True

, x = - 16 W_{0} (- \frac{1}{16})

True

, x = - 16 W_{- 1} (- \frac{1}{16})

True

The solutions are

x = - 16 W_{0} (\frac{1}{16}), x = - 16 W_{0} (- \frac{1}{16}), x = - 16 W_{- 1} (- \frac{1}{16})

lo g_{5} (- 9 - 2 x) = 2

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

lo g_{3} (x) + lo g_{3} (x + 6) = 3

2 lo g_{10} (x) - lo g_{10} (x - 6) = 0

4 lo g_{6} (x) - 2 lo g_{10} (x^{6}) = 7

What is the answer to 8ln(x^2)=x ?
The answer to 8ln(x^2)=x is x=-16\W_{0}(1/16),x=-16\W_{0}(-1/16),x=-16\W_{-1}(-1/16)
Solve for x: 8ln(x^2)=x
The solution is x=-16\W_{0}(1/16),x=-16\W_{0}(-1/16),x=-16\W_{-1}(-1/16)