What is the answer to ln(x^{10})=x ?

The answer to ln(x^{10})=x is x=-10\W_{0}(1/10),x=-10\W_{0}(-1/10),x=-10\W_{-1}(-1/10)

Solve for x: ln(x^{10})=x

The solution is x=-10\W_{0}(1/10),x=-10\W_{0}(-1/10),x=-10\W_{-1}(-1/10)

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ln (x^{10}) = x

x = - 10 W_{0} (\frac{1}{10}), x = - 10 W_{0} (- \frac{1}{10}), x = - 10 W_{- 1} (- \frac{1}{10})

Decimal

x = - 0.91276 \dots, x = 1.11832 \dots, x = 35.77152 \dots

Solution steps

ln (x^{10}) = x

Apply exponent rule:

a^{2 \cdot n} = (a^{2})^{n}

x^{10} = (x^{2})^{5}

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

Apply log rules

ln (x^{2}) = \frac{x}{5}

f (x) = g (x),

then

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

e^{l n (x^{2})} = e^{\frac{x}{5}}

Simplify

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

x^{2} = e^{\frac{x}{5}}

Solve

x^{2} = e^{\frac{x}{5}} : x = - 10 W_{0} (\frac{1}{10}), x = - 10 W_{0} (- \frac{1}{10}), x = - 10 W_{- 1} (- \frac{1}{10})

x = - 10 W_{0} (\frac{1}{10}), x = - 10 W_{0} (- \frac{1}{10}), x = - 10 W_{- 1} (- \frac{1}{10})

Verify Solutions:

x = - 10 W_{0} (\frac{1}{10})

True

, x = - 10 W_{0} (- \frac{1}{10})

True

, x = - 10 W_{- 1} (- \frac{1}{10})

True

The solutions are

x = - 10 W_{0} (\frac{1}{10}), x = - 10 W_{0} (- \frac{1}{10}), x = - 10 W_{- 1} (- \frac{1}{10})

lo g_{10} (x + 3) - lo g_{10} (x) = 2

2 lo g_{10} (x) = 10

lo g_{2} (2 x + 7) = 3

2 ln (x) - 3 ln (\frac{1}{x}) = 10

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

What is the answer to ln(x^{10})=x ?
The answer to ln(x^{10})=x is x=-10\W_{0}(1/10),x=-10\W_{0}(-1/10),x=-10\W_{-1}(-1/10)
Solve for x: ln(x^{10})=x
The solution is x=-10\W_{0}(1/10),x=-10\W_{0}(-1/10),x=-10\W_{-1}(-1/10)