What is the answer to 16ln(x)=log_{x}(e) ?

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

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16ln(x)=log_{x}(e)

16 ln (x) = lo g_{x} (e)

Decimal Notation

x = 1.28402 \dots, x = 0.77880 \dots

Solution steps

16 ln (x) = lo g_{x} (e)

Apply log rules

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

Rewrite the equation with

ln (x) = u

16 u = \frac{1}{u}

Solve

16 u = \frac{1}{u} : u = \frac{1}{4}, u = - \frac{1}{4}

u = \frac{1}{4}, u = - \frac{1}{4}

Substitute back

u = ln (x),

solve for

x

Solve

Verify Solutions:

True

The solutions are

lo g_{5} (lo g_{2} (x)) = 1

y = ln (y) - 1

lo g_{5} (5 x - 1) = lo g_{5} (4 x + 5)

lo g_{3} (lo g_{3} (x + 5)) = 1

12 = ln (\frac{900}{900 - x})

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