What is the answer to 16ln(x)= 1/(ln(x)) ?

The answer to 16ln(x)= 1/(ln(x)) is x=\sqrt[4]{e},x= 1/(\sqrt[4]{e)}

Solve for x: 16ln(x)= 1/(ln(x))

The solution is x=\sqrt[4]{e},x= 1/(\sqrt[4]{e)}

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16 ln (x) = \frac{1}{ln ( x )}

Solution steps

16 ln (x) = \frac{1}{ln ( x )}

Multiply both sides by

ln (x)

16 ln (x) ln (x) = \frac{1}{ln ( x )} ln (x)

Simplify

16 ln (x) ln (x) : 16 ln^{2} (x)

16 ln^{2} (x) = 1

Rewrite the equation with

ln (x) = u

16 u^{2} = 1

Solve

16 u^{2} = 1 : u = \frac{1}{16}, u = - \frac{1}{16}

u = \frac{1}{16}, u = - \frac{1}{16}

Substitute back

u = ln (x),

solve for

x

Solve

Verify Solutions:

True

The solutions are

lo g_{3} (- 2 x - 10) = 2 + lo g_{3} (6)

1.23 = \frac{0.0257}{4} ln (k)

x, ln (2 x + 1) = 2 - ln (x)

lo g_{10} (x - 2) = 1.258

ln (x) = ln (2 x - 3)

What is the answer to 16ln(x)= 1/(ln(x)) ?
The answer to 16ln(x)= 1/(ln(x)) is x=\sqrt[4]{e},x= 1/(\sqrt[4]{e)}
Solve for x: 16ln(x)= 1/(ln(x))
The solution is x=\sqrt[4]{e},x= 1/(\sqrt[4]{e)}